  The Laser Interferometer Gravitational-Wave Observatory, LIGO, found direct
evidence for double black hole binaries emitting gravitational waves. Galactic
nuclei are expected to harbor the densest population of stellar-mass black
holes. A significant fraction ($\sim30\%$) of these black holes can reside in
binaries. We examine the fate of the black hole binaries in active galactic
nuclei, which get trapped in the inner region of the accretion disk around the
central supermassive black hole. We show that binary black holes can migrate
into and then rapidly merge within the disk well within a Salpeter time. The
binaries may also accrete a significant amount of gas from the disk, well above
the Eddington rate. This could lead to detectable X-ray or gamma-ray emission,
but would require hyper-Eddington accretion with a few percent radiative
efficiency, comparable to thin disks. We discuss implications for gravitational
wave observations and black hole population studies. We estimate that Advanced
LIGO may detect $\sim20$ such, gas-induced binary mergers per year.
