We have used four telescopes at different longitudes to obtain near-continuous light-curve coverage of the star HD 80606 as it was transited by its similar to 4-M(jup) planet. The observations were performed during the predicted transit windows around 2008 October 25 and 2009 February 14. Our data set is unique in that it simultaneously constrains the duration of the transit and the planet's period. Our Markov Chain Monte Carlo analysis of the light curves, combined with constraints from radial-velocity data, yields system parameters consistent with previously reported values. We find a planet-to-star radius ratio marginally smaller than previously reported, corresponding to a planet radius of R(p) = 0.921 +/- 0.036R(Jup).