  We measured the system-integrated thermal emission of the binary Kuiper Belt
Object 1999 TC36 at wavelengths near 24 and 70 microns using the Spitzer space
telescope. We fit these data and the visual magnitude using both the Standard
Thermal Model and thermophysical models. We find that the effective diameter of
the binary is 405 km, with a range of 350 -- 470 km, and the effective visible
geometric albedo for the system is 0.079 with a range of 0.055 -- 0.11. The
binary orbit, magnitude contrast between the components, and system mass have
been determined from HST data (Margot et al., 2004; 2005a; 2005b). Our
effective diameter, combined with that system mass, indicate an average density
for the objects of 0.5 g/cm3, with a range 0.3 -- 0.8 g/cm3. This density is
low compared to that of materials expected to be abundant in solid bodies in
the trans-Neptunian region, requiring 50 -- 75% of the interior of 1999 TC36 be
taken up by void space. This conclusion is not greatly affected if 1999 TC36 is
``differentiated'' (in the sense of having either a rocky or just a non-porous
core). If the primary is itself a binary, the average density of that
(hypothetical) triple system would be in the range 0.4 -- 1.1 g/cm3, with a
porosity in the range 15 -- 70%.
