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Photometric monitoring of the gravitational lens system 0957+561A,B in the gand r bands with the Apache Point Observatory (APO) 3.5 m telescope during 1996shows a sharp g band event in the trailing (B) image light curve at the precisetime predicted from the observation of an event during 1995 in the leading (A)image with a delay of 415 days. This success confirms the "short delay," andthe lack of any feature at a delay near 540 days rejects the "long delay" forthis system, resolving a long-standing controversy. A series of statisticalanalyses of our light curve data yield a best fit delay of 417 +/- 3 days (95%confidence interval). Recent improvements in the modeling of the lens system(consisting of a galaxy and cluster) allow us to derive a value of the global(at z = 0.36) value of Hubble's constant H_0 using Refsdal's method, a simpleand direct distance determination based on securely understood physics andgeometry. The result is H_0 = 63 +/- 12 km/s/Mpc (for Omega = 1) where this 95%confidence interval is dominated by remaining lens model uncertainties.Comment: accepted by ApJ, AASTeX 4.0 preprint, 4 PostScript figure

A Robust Determination of the Time Delay in 0957+561A, B and a Measurement of the Global Value of Hubble's Constant