Observed time delays between images of a lensed QSO lead to the determinati
on of the Hubble constant by Refsdal's method, provided the mass distributi
on in the lensing galaxy is reasonably well known. Since the two or four QS
O images usually observed are woefully inadequate by themselves to provide
a unique reconstruction of the galaxy mass, most previous reconstructions h
ave been limited to simple parameterized models, which may lead to large sy
stematic errors in the derived H-0 by failing to consider enough possibilit
ies for the mass distribution of the lens. We use nonparametric modeling of
galaxy lenses to better explore physically plausible but not overly constr
ained galaxy mass maps, all of which reproduce the lensing observables exac
tly, and derive the corresponding distribution of H-0's. Blind tests-in whi
ch one of us simulated galaxy lenses, lensing observables, and a value for
H-0 and the other applied our modeling technique to estimate H-0-indicate t
hat our procedure is reliable. For four simulated lensed QSOs, the distribu
tions of inferred H-0 have an uncertainty of similar or equal to 10% at 90%
confidence. Application to published observations of the two best-constrai
ned time-delay lenses, PG 1115+080 and B1608+656, yields H-0 = 61 +/- 11 km
s(-1) Mpc(-1) at 68% confidence and 61 + 18 km s(-1) Mpc(-1) at 90% confid
ence.