Gravitationally lensed quasars can be used to map the mass distribution in lensing galaxies and to estimate the Hubble constant H-0 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 1.2 m EULER telescope located at La Silla and with the 1.3 m 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 Delta t(B-A) = 35.5 +/- 1.4 days (3.8%) and Delta t(B-C) = 62.6(-2.3)(+4.1) 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 F-A/F-B = 2.88 +/- 0.04, F-A/F-C = 3.38 +/- 0.06, and F-A1/F-A2 = 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 H-0 agrees with the concordance value: non-parametric modeling of the lensing galaxy predicts H-0 = 67(-10)(+13) km s(-1) Mpc(-1), while the Single Isothermal Sphere model yields H-0 = 63(-3)(+7) km s(-1) Mpc(-1) (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.