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Jones et al., Type Ia supernovae (SNe Ia) are more precise standardizable candles when measured in the near-infrared (NIR) than in the optical. With this motivation, from 2012 to 2017 we embarked on the RAISIN program with the Hubble Space Telescope (HST) to obtain rest-frame NIR light curves for a cosmologically distant sample of 37 SNe Ia (0.2 ≲ z ≲ 0.6) discovered by Pan-STARRS and the Dark Energy Survey. By comparing higher-z HST data with 42 SNe Ia at z < 0.1 observed in the NIR by the Carnegie Supernova Project, we construct a Hubble diagram from NIR observations (with only time of maximum light and some selection cuts from optical photometry) to pursue a unique avenue to constrain the dark energy equation-of-state parameter, w. We analyze the dependence of the full set of Hubble residuals on the SN Ia host galaxy mass and find Hubble residual steps of size ∼0.06-0.1 mag with 1.5σ−2.5σ significance depending on the method and step location used. Combining our NIR sample with cosmic microwave background constraints, we find 1 + w = −0.17 ± 0.12 (statistical + systematic errors). The largest systematic errors are the redshift-dependent SN selection biases and the properties of the NIR mass step. We also use these data to measure H0 = 75.9 ± 2.2 km s−1 Mpc−1 from stars with geometric distance calibration in the hosts of eight SNe Ia observed in the NIR versus H0 = 71.2 ± 3.8 km s−1 Mpc−1 using an inverse distance ladder approach tied to Planck. Using optical data, we find 1 + w = −0.10 ± 0.09, and with optical and NIR data combined, we find 1 + w = −0.06 ± 0.07; these shifts of up to ∼0.11 in w could point to inconsistency in the optical versus NIR SN models. There will be many opportunities to improve this NIR measurement and better understand systematic uncertainties through larger low-z samples, new light-curve models, calibration improvements, and eventually by building high-z samples from the Roman Space Telescope., Support for this work was provided by a Gordon and Betty Moore Foundation postdoctoral fellowship to D.O.J.at the University of California, Santa Cruz, and by NASA through the NASA Hubble Fellowship grant HF2-51462.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. The Cambridge University team acknowledges support from the European Research Council under the European Union’s Horizon 2020 research and innovation program (ERC grant agreement No. 101002652); the ASTROSTAT-II collaboration, enabled by the Horizon 2020, EU grant agreement No. 873089; and the Cambridge Centre for Doctoral Training in Data-Intensive Science funded by the UK Science and Technology Facilities Council (STFC). L.G. acknowledges financial support from the Spanish Ministerio de Ciencia e Innovación (MCIN), the Agencia Estatal de Investigación (AEI) 10.13039/ 501100011033, and the European Social Fund (ESF) “Investing in your future” under the 2019 Ramón y Cajal program RYC2019027683-I and the PID2020-115253GA-I00 HOSTFLOWS project, from Centro Superior de Investigaciones Científicas (CSIC) under the PIE project 20215AT016, and the program Unidad de Excelencia Mara de Maeztu CEX2020-001058-M. M. R.S. is supported by the NSF Graduate Research Fellowship Program under grant 1842400. The UCSC team is supported in part by NASA grants 14-WPS14-0048, NNG16PJ34C, and NNG17PX03C; NSF grants AST-1518052 and AST-1815935; NASA through grant No. AR-14296 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; and fellowships from the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation to R.J.F. Based on observations with the NASA/ESA Hubble Space Telescope obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for program Nos. 13046 and 14216 was provided through grants from the STScI under NASA contract NAS5-26555. The Carnegie Supernova Project has been supported by the National Science Foundation under grants AST0306969, AST0607438, AST1008343, AST1613426, AST1613455, and AST1613472. L.K. thanks the UKRI Future Leaders Fellowship for support through the grant MR/T01881X/ 1. 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.