We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-massblack holes. The signal, GW151226, was observed by the twin detectors of the Laser InterferometerGravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initiallyidentified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-lineanalyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than5σ. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency andamplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of3.4+0.7−0.9 × 10^(−22). The inferred source-frame initial black hole masses are 14.2+8.3−3.7M⊙ and 7.5+2.3−2.3M⊙,and the final black hole mass is 20.8+6.1−1.7M⊙.We find that at least one of the component black holes has spingreater than 0.2. This source is located at a luminosity distance of 440+180−190 Mpc corresponding to a redshiftof 0.09+0.03−0.04 . All uncertainties define a 90% credible interval. This second gravitational-wave observationprovides improved constraints on stellar populations and on deviations from general relativity.