Previous high-resolution cosmological simulations predicted that the first stars to appear in the early universe were very massive and formed in isolation. Here, we discuss a cosmological simulation in which the central 50 M(o) (where M(o) is the mass of the Sun) clump breaks up into two cores having a mass ratio of two to one, with one fragment collapsing to densities of 10(-8) grams per cubic centimeter. The second fragment, at a distance of approximately 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 approximately 10(5) years and will likely form a binary star system.