  Although dwarf carbon (dC) stars are thought universally to be binaries to
explain the presence of $C_2$ in their spectra while still near main sequence
luminosity, direct observational evidence for binarity is remarkably scarce.
Here we report the detection of a 2.92 d periodicity in both photometry and
radial velocity of SDSS J125017.90+252427.6, an $r=16.4$ dC star. This is the
first photometric binary dC, and only the second dC spectroscopic binary. The
relative phase of the photometric period to the spectroscopic observations
suggests that the photometric variations are a reflection effect due to heating
from an unseen companion. The observed radial velocity amplitude of the dC
component ($K = 98.8\pm10.7$ km/s) is consistent with a white dwarf companion,
presumably the evolved star that earlier donated the carbon to the dC, although
substantial orbital evolution must have occurred. Large synoptic photometric
surveys such as the Palomar Transient Factory, used for this work, may prove
useful for identifying binaries among the shorter period dC stars.
