We have measured the separations and position angles of the two components of the binary trans-Neptunian object (58534) 1997 CQ(29) at eight epochs. From these data we are able to constrain the orbit and mass of this binary system. The best-fitting orbit has an orbital period of P = 312 +/- 3 days. The orbital eccentricity is e 0.45 +/- 0.03 and the semimajor axis is a = 8010 +/- 80 km. The mass of the system is surprisingly low at (0.42 +/- 0.02) x 10(18) kg. To account for the observed brightness consistent with the low mass and a range of plausible densities, the geometric albedo must be very high; for an assumed density of 1000 kg m(-3), we find a red geometric albedo of p(R) = 0.37, an order of magnitude higher than has been generally assumed for trans-Neptunian objects. If objects with comparably high albedos are common in the Kuiper belt, estimates of the mass of the belt must be significantly reduced. The semimajor axis of (58534) 1997 CQ(29)'s orbit is 2.8% of the Hill radius of the primary, a value strikingly similar to this same ratio in other trans-Neptunian binaries, main-belt binaries, and regular satellite systems.