Apollo asteroid 1999 YC may share a dynamical association with the Phaethon-Geminid stream complex (Ohtsuka et al. 2008). Here, we present photometric observations taken to determine the physical properties of 1999 YC. The object shows a nearly neutral reflection spectrum, similar to but slightly redder than related objects 3200 Phaethon and 2005 UD. Assuming an albedo equal to 3200 Phaethons we find that the diameter is 1.4+/-0.1 km. Time-resolved broad-band photometry yields a double-peaked rotational period of 4.4950+/-0.0010 hr while the range of the lightcurve indicates an elongated shape having a projected axis ratio near 1.9:1. Surface brightness models provide no evidence of lasting mass loss of the kind seen in active short period cometary nuclei. An upper limit to the mass loss is set at about 0.001 kg/s, corresponding to an upper limit on the fraction of the surface that could be sublimating water ice of 0.001. If sustained over the 1000 yr age of the Geminid stream, the total mass loss from 1999 YC (3e7 kg) would be small compared to the reported stream mass (1e12 - 1e13 kg), suggesting that the stream is the product of catastrophic, rather than steady-state, breakup of the parent object.