  We show that a black-hole binary with an external companion can undergo
Lidov-Kozai cycles that cause a close pericenter passage, leading to a rapid
merger due to gravitational-wave emission. This scenario occurs most often for
systems in which the companion has mass comparable to the reduced mass of the
binary and the companion orbit has semi-major axis within a factor of $\sim 10$
of the binary semi-major axis. Using a simple population-synthesis model and
3-body simulations, we estimate the rate of mergers in triple black hole
systems in the field to be about six per Gpc$^3$ per year in the absence of
natal kicks during black hole formation. This value is within the low end of
the 90\% credible interval for the total black-hole black-hole merger rate
inferred from the current LIGO results. There are many uncertainties in these
calculations, the largest of which is the unknown distribution of natal kicks.
Even modest natal kicks of $40\mbox{km s}^{-1}$ will reduce the merger rate by
a factor of 40. A few percent of these systems will have eccentricity greater
than 0.999 when they first enter the frequency band detectable by aLIGO (above
10 Hz).
