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 11E0435-1223 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 Ho. 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(-8.3)(+9.4) km s(-1) Mpc(-1) for PG 1115+080, H-0 = 70.1(-4.5)(+5.3) km s(-1) Mpc(-1) for HE 0435-1223, and H-0 = 77.0(-4.6)(+4.0) km s(-1) Mpc(-1) for RXJ 1131-1231. The joint AO-only result for the three lenses is H-0 = 75.6(-3.3)(+3.2) 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) km s(-1) Mpc(-1). All of these results assume a flat A cold dark matter cosmology with a uniform prior on Omega(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.