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 $31.2_{-6.0}^{+8.4}{M}_{\odot }$ and $19.4_{-5.9}^{+5.3}{M}_{\odot }$ (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, ${\chi }_{\mathrm{eff}}=-0.12_{-0.30}^{+0.21}$. This result implies that spin configurations with both component spins positively aligned with the orbital angular momentum are disfavored. The source luminosity distance is $880_{-390}^{+450}\mathrm{Mpc}$ 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 $m_g\le 7.7\times {10}^{-23}\mathrm{eV}/c^2$. In all cases, we find that GW170104 is consistent with general relativity.