Gravitationally lensed quasars can be used to map the mass distribution in lensing galaxies and to estimate the Hubble constant H0 by measuring the time delays between the quasar images. Here we report the measurement of two independent time delays in the quadruply imaged quasar WFI J2033-4723 (z=1.66). Our data consist of R-band images obtained with the Swiss 1.2m EULER telescope located at La Silla and with the 1.3m SMARTS telescope located at Cerro Tololo. The light curves have 218 independent epochs spanning 3 full years of monitoring between March 2004 and May 2007, with a mean temporal sampling of one observation every 4th day. We measure the time delays using three different techniques, and we obtain Dt(B-A)=35.5+/-1.4days (3.8%) and Dt(B-C)=62.6^+4.1^_-2.3_days (^+6.5%^_-3.7%_), where A is a composite of the close, merging image pair. After correcting for the time delays, we find R-band flux ratios of FA/FB=2.88+/-0.04, FA/FC=3.38+/-0.06, and FA1/FA2=1.37+/-0.05 with no evidence for microlensing variability over a time scale of three years. However, these flux ratios do not agree with those measured in the quasar emission lines, suggesting that longer term microlensing is present. Our estimate of H0 agrees with the concordance value: non-parametric modeling of the lensing galaxy predicts H0=67^+13^_-10_km/s/Mpc, while the Single Isothermal Sphere model yields H0=63^+7^_-3_km/s/Mpc (68% confidence level). More complex lens models using a composite de Vaucouleurs plus NFW galaxy mass profile show twisting of the mass isocontours in the lensing galaxy, as do the non-parametric models. As all models also require a significant external shear, this suggests that the lens is a member of the group of galaxies seen in field of view of WFI J2033-4723.