We present first results from five years of spectrophotometric monitoring of the bright double QSO and gravitational lens HE 1104-1805. The quasar has varied considerably over this time, while the emission line fluxes appear to have remained constant. We have constructed monochromatic continuum light curves for components A and B, finding that B leads the variability. A quantitative analysis with the Pelt method gives a best estimate for the light travel time delay of about 0.73 years, although a value as low as 0.3 cannot yet be excluded. We discuss possible models for the QSO-lens configuration and use our measured time delay to predict the redshift of the lens, z_d. Finding that most likely z_d ≲ 1, we can rule out the hitherto favoured values of z_d = 1.32 or 1.66. A new candidate is an absorption system at z = 0.73, but the lens could also be an elliptical not detected in absorption.