Hubble Space Telescope observations between 2001 and 2010 resolved the binary components of the Cold Classical transneptunian object (79360) Sila-Nunam (provisionally designated 1997 CS29). From these observations we have determined the circular, retrograde mutual orbit of Nunam relative to Sila with a period of 12.50995 ± 0.00036 days and a semimajor axis of 2777 ± 19 km. A multi-year season of mutual events, in which the two near-equal brightness bodies alternate in passing in front of one another as seen from Earth, is in progress right now, and on 2011 February 1 UT, one such event was observed from two different telescopes. The mutual event season offers a rich opportunity to learn much more about this barely-resolvable binary system, potentially including component sizes, colors, shapes, and albedo patterns. The low eccentricity of the orbit and a photometric lightcurve that appears to coincide with the orbital period are consistent with a system that is tidally locked and synchronized, like the Pluto-Charon system. The orbital period and semimajor axis imply a system mass of (10.84 ± 0.22) × 1018 kg, which can be combined with a size estimate based on Spitzer and Herschel thermal infrared observations to infer an average bulk density of 0.72-0.23+0.37 g cm, comparable to the very low bulk densities estimated for small transneptunian binaries of other dynamical classes.