The Daya Bay Reactor Neutrino Experiment has measured a non-zero value for the neutrino mixing angle θ13 with a significance of 7.7 standard deviations. Antineutrinos from six 2.9 GWth reactors were detected in six antineutrino detectors deployed in two near and one far underground experimental halls. With a 116.8 kton-GWth-day live-time exposure in 139 days, 28,909 (205,308) electron-antineutrino candidates were detected at the far hall (near hall). The ratio of the observed to expected number of antineutrinos at the far hall is R = 0.944 ± 0.007 ± 0.003 (syst). A rate-only analysis finds sin22θ13 = 0.089 ± 0.010 (stat) ± 0.005 (syst) in a three-neutrino framework.