We describe the observation of GW170104, a gravitational-wave signal produced by the coalescence of a pair of stellar-mass black holes. The signal was measured on January 4, 2017 at 10: 11: 58.6 UTC by the twin advanced detectors of the Laser Interferometer Gravitational-Wave Observatory during their second observing run, with a network signal-to-noise ratio of 13 and a false alarm rate less than 1 in 70 000 years. The inferred component black hole masses are 31.2(-6.0)(+8.4) M-circle dot and 19.4(-5.9)(+5.3)M(circle dot) (at the 90\% credible level). The black hole spins are best constrained through measurement of the effective inspiral spin parameter, a mass-weighted combination of the spin components perpendicular to the orbital plane, chi(eff) = -0.12(-0.30)(+0.21) . This result implies that spin configurations with both component spins positively aligned with the orbital angular momentum are disfavored. The source luminosity distance is 880(-390)(+450) Mpc corresponding to a redshift of z = 0.18(-0.07)(+0.08) . We constrain the magnitude of modifications to the gravitational-wave dispersion relation and perform null tests of general relativity. Assuming that gravitons are dispersed in vacuum like massive particles, we bound the graviton mass to m(g) <= 7.7 x 10(-23) eV/c(2). In all cases, we find that GW170104 is consistent with general relativity.