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We present the measurement of the Hubble Constant, $H_0$, with three stronggravitational lens systems. We describe a blind analysis of both PG1115+080 andHE0435-1223 as well as an extension of our previous analysis of RXJ1131-1231.For each lens, we combine new adaptive optics (AO) imaging from the KeckTelescope, obtained as part of the SHARP AO effort, with Hubble Space Telescope(HST) imaging, velocity dispersion measurements, and a description of theline-of-sight mass distribution to build an accurate and precise lens massmodel. This mass model is then combined with the COSMOGRAIL measured timedelays in these systems to determine $H_{0}$. We do both an AO-only and anAO+HST analysis of the systems and find that AO and HST results are consistent.After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~\rmkm\,s^{-1}\,Mpc^{-1}$ for PG1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~\rmkm\,s^{-1}\,Mpc^{-1}$ for HE0435-1223, and $H_{0}=77.0^{+4.0}_{-4.6}~\rmkm\,s^{-1}\,Mpc^{-1}$ for RXJ1131-1231. The joint AO-only result for the threelenses is $H_{0}=75.6^{+3.2}_{-3.3}~\rm km\,s^{-1}\,Mpc^{-1}$. The joint resultof the AO+HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~\rmkm\,s^{-1}\,Mpc^{-1}$. All of the above results assume a flat $\Lambda$ colddark matter cosmology with a uniform prior on $\Omega_{\textrm{m}}$ in [0.05,0.5] and $H_{0}$ in [0, 150] $\rm km\,s^{-1}\,Mpc^{-1}$. This work is acollaboration of the SHARP and H0LiCOW teams, and shows that AO data can beused as the high-resolution imaging component in lens-based measurements of$H_0$. The full time-delay cosmography results from a total of six stronglylensed systems are presented in a companion paper.

A SHARP view of H0LiCOW: $H_{0}$ from three time-delay gravitational lens systems with adaptive optics imaging