  Previous high resolution cosmological simulations predict the first stars to
appear in the early universe to be very massive and to form in isolation. Here
we discuss a cosmological simulation in which the central 50 solar mass clump
breaks up into two cores, having a mass ratio of two to one, with one fragment
collapsing to densities of 10^{-8} g/cc. The second fragment, at a distance of
800 astronomical units, is also optically thick to its own cooling radiation
from molecular hydrogen lines, but is still able to cool via collision-induced
emission. The two dense peaks will continue to accrete from the surrounding
cold gas reservoir over a period of 10^5 years and will likely form a binary
star system.
