  We conducted a search for very short-period transiting objects in the
publicly available Kepler dataset. Our preliminary survey has revealed four
planetary candidates, all with orbital periods less than twelve hours. We have
analyzed the data for these candidates using photometric models that include
transit light curves, ellipsoidal variations, and secondary eclipses to
constrain the candidates' radii, masses, and effective temperatures. Even with
masses of only a few Earth masses, the candidates' short periods mean they may
induce stellar radial velocity signals (a few m/s) detectable by currently
operating facilities. The origins of such short-period planets are unclear, but
we discuss the possibility that they may be the remnants of disrupted hot
Jupiters. Whatever their origins, if confirmed as planets, these candidates
would be among the shortest-period planets ever discovered. Such planets would
be particularly amenable to discovery by the planned TESS mission.
