We present an implementation of the Gehrels et al. galaxy-targeted strategy for gravitational-wave (GW) follow-up using the Las Cumbres Observatory global network of telescopes. We use the Galaxy List for the Advanced Detector Era (GLADE) galaxy catalog, which we show is complete (with respect to a Schechter function) out to ∼300 Mpc for galaxies brighter than the median Schechter function galaxy luminosity. We use a prioritization algorithm to select the galaxies with the highest chance of containing the counterpart given their luminosity, their position, and their distance relative to a GW localization, and in which we are most likely to detect a counterpart given its expected brightness compared to the limiting magnitude of our telescopes. This algorithm can be easily adapted to any expected transient parameters and telescopes. We implemented this strategy during the second Advanced Detector Observing Run (O2) and followed the black hole merger GW170814 and the neutron star merger GW170817. For the latter, we identified an optical kilonova/macronova counterpart thanks to our algorithm selecting the correct host galaxy fifth in its ranked list among the 182 galaxies we identified in the Laser Interferometer Gravitational-wave Observatory (LIGO)/Virgo localization. This also allowed us to obtain some of the earliest observations of the first optical transient ever triggered by a GW detection (as presented in a companion paper).