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 1998 April and 1999 November. 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 Deltat = 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 Mailer et al., this time delay estimate yields a Hubble parameter of H-0 = 52(-8)(+14) 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.