We present optical I-band light curves of the gravitationally lensed double QSO B1600+434 from observations obtained at the Nordic Optical Telescope (NOT) between April 1998 and November 1999. The photometry has been performed by simultaneous deconvolution of all the data frames, involving a numerical lens galaxy model. Four methods have been applied to determine the time delay between the two QSO components, giving a mean estimate of Delta_t = 51+/-4 days (95% confidence level). This is the fourth optical time delay ever measured. Adopting a Omega=0.3, Lambda=0 Universe and using the mass model of Maller et al. (2000), this time-delay estimate yields a Hubble parameter of H_0=52 (+14, -8) km s^-1 Mpc^-1 (95% confidence level) where the errors include time-delay as well as model uncertainties. There are time-dependent offsets between the two (appropriately shifted) light curves that indicate the presence of external variations due to microlensing.