It is often assumed that gravitational-wave (GW) events resulting from the merger of stellar-mass black holes are unlikely to produce electromagnetic (EM) counterparts. We point out that the progenitor binary has probably shed a mass 10 M during its prior evolution. If even a tiny fraction of this gas is retained in a circumbinary disk, the sudden mass loss and recoil of the merged black hole shocks and heats it within hours of the GW event. Whether the resulting EM signal is detectable is uncertain. The optical depth through the disk is likely to be high enough that the prompt emission consists only of photons from its optically thin skin, while the majority may take years to emerge. However, if some mechanism can release more photons in a time comparable to the few-hour energy production time, the peak luminosity of the EM signal could be detectable. For a disk retaining only ∼10−3 of the mass shed in the earlier binary evolution, medium-energy X-rays to infrared emission would be observable hours after the GW event for source distances of ∼500 Mpc. Events like this may already have been observed, but ascribed to unidentified active galactic nuclei. Improved sky localization should eventually allow identification based on spatial coincidence. A detection would provide unique constraints on formation scenarios and potentially offer tests of strong-field general relativity. Accordingly, we argue that the high scientific payoff of an EM detection fully justifies search campaigns.