K.A.P., M.W.-V., and L.G. were supported in part by the US National Science Foundation under grant AST-1311862. K.A. P. additionally acknowledges support from PITT PACC. K.A. P. was also supported in part by the Berkeley Center for Cosmological Physics and the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under contract No. DE-AC02-05CH11231 and U.S. Department of Energy Office of Science under contract No. DE-AC02-76SF00515. L.G. was additionally funded in part by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 839090. We thank the referee, whose comments have improved this paper, and Saurabh Jha, Kyle Boone, and Ravi Gupta for useful conversations. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is www.sdss.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration, including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofisica de Canarias, Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut fur Astrophysik Potsdam (AIP), Max-Planck-Institut fur Astronomie (MPIA Heidelberg), Max-Planck-Institut fur Astrophysik (MPA Garching), Max-Planck-Institut fur Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatario Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autonoma de Mexico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University. This research uses services or data provided by the Astro Data Lab at NSF's National Optical-Infrared Astronomy Research Laboratory. NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under a cooperative agreement with the National Science Foundation. The Legacy Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS; Proposal ID #2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID #2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey). DECaLS, BASS, and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, NSF's NOIRLab; the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOIRLab. The Legacy Surveys project is honored to be permitted to conduct astronomical research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation. This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at The Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at UrbanaChampaign, the Institut de Ciencies de l'Espai (IEEC/CSIC), the Institut de Fisica d'Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, NSF's NOIRLab, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas A&M University. The Legacy Survey team makes use of data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by the National Aeronautics and Space Administration. The Legacy Surveys imaging of the DESI footprint is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under contract No. DE-AC02-05CH1123; by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract; and by the U.S. National Science Foundation, Division of Astronomical Sciences under contract No. AST-0950945 to NOAO. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts., We analyze 143 Type Ia supernovae (SNe Ia) observed in H band (1.6-1.8 mu m) and find that SNe Ia are intrinsically brighter in H band with increasing host galaxy stellar mass. We find that SNe Ia in galaxies more massive than 10(10)(.4)(3) M-circle dot are 0.13 +/- 0.04 mag brighter in H than SNe Ia in less massive galaxies. The same set of SNe Ia observed at optical wavelengths, after width-color-luminosity corrections, exhibit a 0.10 +/- 0.03 mag offset in the Hubble residuals. We observe an outlier population (vertical bar Delta H-max vertical bar > 0.5 mag) in the H band and show that removing the outlier population moves the mass threshold to 10(10.65) M-circle dot and reduces the step in H band to 0.08 +/- 0.04 mag, but the equivalent optical mass step is increased to 0.13 +/- 0.04 mag. We conclude that the outliers do not drive the brightness-host-mass correlation. Less massive galaxies preferentially host more higher-stretch SNe Ia, which are intrinsically brighter and bluer. It is only after correction for width-luminosity and color- luminosity relationships that SNe Ia have brighter optical Hubble residuals in more massive galaxies. Thus, finding that SNe Ia are intrinsically brighter in H in more massive galaxies is an opposite correlation to the intrinsic (prewidth-luminosity correction) optical brightness. If dust and the treatment of intrinsic color variation were the main driver of the host galaxy mass correlation, we would not expect a correlation of brighter H-band SNe Ia in more massive galaxies., National Science Foundation (NSF) AST-1311862, PITT PACC, Berkeley Center for Cosmological Physics, United States Department of Energy (DOE) DE-AC02-05CH11231 DE-AC02-05CH1123 DE-AC02-76SF00515, European Commission 839090, National Aeronautics & Space Administration (NASA), Alfred P. Sloan Foundation, United States Department of Energy (DOE), Participating Institutions, Center for High-Performance Computing at the University of Utah, SDSS Collaboration, including the Brazilian Participation Group, Carnegie Institution for Science, Carnegie Mellon University, Chilean Participation Group, French Participation Group, Smithsonian Institution, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofisica de Canarias, Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Leibniz Institut fur Astrophysik Potsdam (AIP), Max-Planck-Institut fur Astronomie (MPIA Heidelberg) Max-Planck-Institut fur Astrophysik (MPA Garching) Max-Planck-Institut fur Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatario Nacional/MCTI, Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autonoma de Mexico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, Yale University, National Science Foundation (NSF), Spanish Government, UK Research & Innovation (UKRI), Science & Technology Facilities Council (STFC), Higher Education Funding Council for England, National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, Kavli Institute of Cosmological Physics at the University of Chicago, Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Inovacao e Pesquisa (Finep), Fundacao Carlos Chagas Filho de Amparo Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio De Janeiro (FAPERJ), Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ), German Research Foundation (DFG), Collaborating Institutions in the Dark Energy Survey, National Energy Research Scientific Computing Center, National Science Foundation (NSF) NSF - Directorate for Mathematical & Physical Sciences (MPS) AST-0950945, Association of Universities for Research in Astronomy, Inc., under NASA NAS5-26555 National Aeronautics & Space Administration (NASA) NNX09AF08G