Kepler-79 (KOI-152) has four planetary candidates ranging in size from 3.5 to 7 times the size of the Earth, in a compact configuration with orbital periods near a 1:2:4:6 chain of commensurability, from 13.5 to 81.1 days. All four planets exhibit transit timing variations with periods that are consistent with the distance of each planet to resonance with its neighbors. We perform a dynamical analysis of the system based on transit timing measurements over 1282 days of Kepler photometry. Stellar parameters are obtained using a combination of spectral classification and the stellar density constraints provided by light curve analysis and orbital eccentricity solutions from our dynamical study. Our models provide tight bounds on the masses of all four transiting bodies, demonstrating that they are planets and that they orbit the same star. All four of Kepler-79's transiting planets have low densities given their sizes, which is consistent with other studies of compact multiplanet transiting systems. The largest of the four, Kepler-79 d (KOI-152.01), has the lowest bulk density yet determined among sub-Saturn mass planets.