We present the measurement of the Hubble Constant, $H_0$, with three strong
gravitational lens systems. We describe a blind analysis of both PG1115+080 and
HE0435-1223 as well as an extension of our previous analysis of RXJ1131-1231.
For each lens, we combine new adaptive optics (AO) imaging from the Keck
Telescope, obtained as part of the SHARP 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 PG1115+080, $H_0=70.1^+5.3_-4.5~\rm
km\,s^-1\,Mpc^-1$ for HE0435-1223, and $H_0=77.0^+4.0_-4.6~\rm
km\,s^-1\,Mpc^-1$ for RXJ1131-1231. The joint AO-only result for the three
lenses is $H_0=75.6^+3.2_-3.3~km\,s^-1\,Mpc^-1$. 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 the above results assume a flat $Łambda$ cold
dark matter cosmology with a uniform prior on $Ømega_m$ in 0.05,
0.5 and $H_0$ in 0, 150 $km\,s^-1\,Mpc^-1$. 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.