A search for light sterile neutrino mixing was performed with the first 217 days of data from the Daya Bay Reactor Antineutrino Experiment. The experiment's unique configuration of multiple baselines from six 2.9 GW(th) nuclear reactors to six antineutrino detectors deployed in two near (effective baselines 512 m and 561 m) and one far (1579 m) underground experimental halls makes it possible to test for oscillations to a fourth (sterile) neutrino in the 10(-3) eV(2)<|Δm(41)(2) |< 0.3 eV(2) range. The relative spectral distortion due to the disappearance of electron antineutrinos was found to be consistent with that of the three-flavor oscillation model. The derived limits on sin(2) 2θ(14) cover the 10(-3) eV(2) ≲ |Δm(41)(2)| ≲ 0.1 eV(2) region, which was largely unexplored.