  We study black hole MACHO binary formation through three-body interactions in
the early universe at $t\sim 10^{-5}$s. The probability distribution functions
of the eccentricity and the semimajor axis of binaries as well as of the
coalescence time are obtained assuming that the black holes are randomly formed
in space. We confirm that the previous order-of-magnitude estimate for the
binary parameters is valid within $\sim 50%$ error. We find that the
coalescence rate of the black hole MACHO binaries is $\sim 5 \times 10^{-2}
\times 2^{\pm 1}$ events/year/galaxy taking into consideration several possible
factors which may affect this estimate. This suggests that the event rate of
coalescing binary black holes will be at least several events per year within
15 Mpc. The first LIGO/VIRGO interferometers in 2001 will be able to verify
whether the MACHOs are black holes or not.
