On August 14, 2017 at 10 30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm rate of 1 in 27 000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are 30.5-3.0+5.7M and 25.3-4.2+2.8M (at the 90% credible level). The luminosity distance of the source is 540-210+130 Mpc, corresponding to a redshift of z=0.11-0.04+0.03. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg2 using only the two LIGO detectors to 60 deg2 using all three detectors. For the first time, we can test the nature of gravitational-wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.