Binary black hole (BBH) mergers found by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors are of immense scientific interest to the astrophysics community, but are considered unlikely to be sources of electromagnetic emission. To test whether they have rapidly fading optical counterparts, we used the Dark Energy Camera to perform an i-band search for the BBH merger GW170814, the first gravitational wave (GW) detected by three interferometers. The 87 deg2 localization region (at 90% confidence) centered in the Dark Energy Survey (DES) footprint enabled us to image 86% of the probable sky area to a depth of i ~ 23 mag and provide the most comprehensive data set to search for electromagnetic (EM) emission from BBH mergers. To identify candidates, we perform difference imaging with our search images and with templates from pre-existing Dark Energy Survey (DES) images. The analysis strategy and selection requirements were designed to remove supernovae and to identify transients that decline in the first two epochs. We find two candidates, each of which is spatially coincident with a star or a high-redshift galaxy in the DES catalogs, and they are thus unlikely to be associated with GW170814. Our search finds no candidates associated with GW170814, disfavoring rapidly declining optical emission from BBH mergers brighter than i ~ 23 mag (L optical ~ 5 × 1041 erg s−1) 1–2 days after coalescence. In terms of GW sky map coverage, this is the most complete search for optical counterparts to BBH mergers to date.