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{\^}+8.4M_⊙ and 19.4_-5.9{\^}+5.3M_⊙ (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, χ_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≤7.7×10{\^}-23  eV/c{\^}2. In all cases, we find that GW170104 is consistent with general relativity.