Massive black holes are found to be ubiquitous in the nuclei of nearby
galaxies, and their growth and evolution appear to be closely linked
to that of their hosts. "Binary" black holes are also predicted to
exist. The paradigm is that massive black holes, hidden in the nuclei
of merging galaxies, would pair inside the violently relaxed core of
the newly formed systems, and form a binary under the action of
gas--dynamical and gravitational torques.  Further hardening
would bring the binary to such a close orbit (of months to a few
light-days across) that gravitational waves would drive the final
black hole coalescence, within less than a Hubble time. Through their
loud gravitational wave emission, their is the hope to weight black
hole masses and spins, but also to witness the cosmic assembly of
galaxies.  This is the reason why massive black hole coalescence events
are considered to be primary target for the planned Laser
Interferometer Space Antenna.  So far it has not been possible to
show that black hole binaries are a natural outcome of galaxy
mergers. The sequence and timing of events that lead to the formation
of a binary in the nuclei of galaxies is poorly known due to the
difficulty of modeling stellar and gas dynamical processes over more
than ten orders of magnitude in density.  Here we report the
first hydrodynamical simulations that show the formation of a massive
black hole binary, following a galaxy-galaxy collision. The
simulations track the orbital evolution of the black hole pair from
the initial stage of the merger between two gas-rich galaxies a
hundred thousand light years apart, to a final separation of only a
few light years. We show that a few million years after the merger is
completed, a binary forms owing to the action of dynamical friction in
a thick, turbulent, gaseous nuclear disk. The disk forms as a result
of the dramatic gas inflow that ensues during the last stage of the
merger, and is heated by a major starburst. We also show that
energetic feedback on the surrounding disk, from the two black holes
while they are spiraling inward must be negligible, otherwise
dynamical friction against such a bloated hot gas would be inefficient
and binary formation early aborted. Double AGN activity comes as a natural
outcome of a merger and will be discussed in light of our findings.