We use Kepler short-cadence light curves to constrain the oblateness of planet candidates in the Kepler sample. The transits of rapidly rotating planets that are deformed in shape will lead to distortions in the ingress and egress of their light curves. We report the first tentative detection of an oblate planet outside the solar system, measuring an oblateness of 0.22–0.11+0.11 for the 18 MJ mass brown dwarf Kepler 39b (KOI 423.01). We also provide constraints on the oblateness of the planets (candidates) HAT-P-7b, KOI 686.01, and KOI 197.01 to be <0.067, <0.251, and <0.186, respectively. Using the Q' values from Jupiter and Saturn, we expect tidal synchronization for the spins of HAT-P-7b, KOI 686.01, and KOI 197.01, and for their rotational oblateness signatures to be undetectable in the current data. The potentially large oblateness of KOI 423.01 (Kepler 39b) suggests that the Q' value of the brown dwarf needs to be two orders of magnitude larger than that of the solar system gas giants to avoid being tidally spun down.