  We present optical lightcurves of the gravitationally lensed components A
(=A1+A2+A3) and B of the quadruple quasar RX J0911.4+0551 (z = 2.80). The
observations were primarily obtained at the Nordic Optical Telescope between
1997 March and 2001 April and consist of 74 I-band data points for each
component. The data allow the measurement of a time delay of 146 +- 8 days (2
sigma) between A and B, with B as the leading component. This value is
significantly shorter than that predicted from simple models and indicates a
very large external shear. Mass models including the main lens galaxy and the
surrounding massive cluster of galaxies at z = 0.77, responsible for the
external shear, yield H_0 = 71 +- 4 (random, 2 sigma) +- 8 (systematic)
km/s/Mpc. The systematic model uncertainty is governed by the surface-mass
density (convergence) at the location of the multiple images.
