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We present the measurement of the Hubble constant, H 0, with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435−1223 as well as an extension of our previous analysis of RXJ 1131−1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL-measured time delays in these systems to determine H 0. We do both an AO-only and an AO + HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives |$H_{0}=82.8^{+9.4}_{-8.3}~\rm km\, s^{-1}\, Mpc^{-1}$| for PG 1115+080, |$H_{0}=70.1^{+5.3}_{-4.5}~\rm km\, s^{-1}\, Mpc^{-1}$| for HE 0435−1223, and |$H_{0}=77.0^{+4.0}_{-4.6}~\rm km\, s^{-1}\, Mpc^{-1}$| for RXJ 1131−1231. The joint AO-only result for the three lenses is |$H_{0}=75.6^{+3.2}_{-3.3}~\rm km\, s^{-1}\, Mpc^{-1}$|⁠. The joint result of the AO + HST analysis for the three lenses is |$H_{0}=76.8^{+2.6}_{-2.6}~\rm km\, s^{-1}\, Mpc^{-1}$|⁠. All of these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ωm in [0.05, 0.5] and H 0 in [0, 150] |$\rm km\, s^{-1}\, Mpc^{-1}$|⁠. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of H 0. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper. [ABSTRACT FROM AUTHOR]