  We perform a set of cosmological simulations of early structure formation
with incorporating baryonic streaming motions. We present a case where a
significantly elongated gas cloud with $\sim\!10^4\,$solar masses (${\rm
M_\odot}$) is formed in a pre-galactic ($\sim\!10^7\,{\rm M_\odot}$) dark halo.
The gas streaming into the halo compresses and heats the massive filamentary
cloud to a temperature of $\sim\!10,000\,$Kelvin. The gas cloud cools rapidly
by atomic hydrogen cooling, and then by molecular hydrogen cooling down to
$\sim\!400\,$Kelvin. The rapid decrease of the temperature and hence of the
Jeans mass triggers fragmentation of the filament to yield multiple gas clumps
with a few hundred solar masses. We estimate the mass of the primordial star
formed in each fragment by adopting an analytic model based on a large set of
radiation hydrodynamics simulations of protostellar evolution. The resulting
stellar masses are in the range of $\sim\!50$-$120\,{\rm M_\odot}$. The massive
stars gravitationally attract each other and form a compact star cluster. We
follow the dynamics of the star cluster using a hybrid $N$-body simulation. We
show that massive star binaries are formed in a few million years through
multi-body interactions at the cluster center. The eventual formation of the
remnant black holes will leave a massive black hole binary, which can be a
progenitor of strong gravitational wave sources similar to those recently
detected by the Advanced Laser Interferometer Gravitational-Wave Observatory
(LIGO).
