  We explore the possibility for the formation of Population III binaries. The
collapse of a rotating cylinder is simulated with a three-dimensional,
high-resolution nested grid, assuming the thermal history of primordial gas.
The simulations are done with dimensionless units, and the results are
applicable to low-mass as well as massive systems by scaling with the initial
density. We find that if the initial angular momentum is as small as $\beta
\approx 0.1$, where $\beta$ is the ratio of centrifugal force to pressure
force, then the runaway collapse of the cloud stops to form a
rotationally-supported disk. After the accretion of the envelope, the disk
undergoes a ring instability, eventually fragmenting into a binary. If the
initial angular momentum is relatively large, a bar-type instability arises,
resulting in the collapse into a single star through rapid angular momentum
transfer. The present results show that a significant fraction of Pop III stars
are expected to form in binary systems, even if they are quite massive or less
massive. The cosmological implications of Population III binaries are briefly
discussed.
