  Future microwave sky surveys will have the sensitivity to detect the
kinematic Sunyaev-Zeldovich signal from moving galaxy clusters, thus providing
a direct measurement of their line-of-sight peculiar velocity. We show that
cluster peculiar velocity statistics applied to foreseeable surveys will put
significant constraints on fundamental cosmological parameters. We consider
three statistical quantities that can be constructed from a cluster peculiar
velocity catalog: the probability density function, the mean pairwise streaming
velocity, and the pairwise velocity dispersion. These quantities are applied to
an envisioned data set which measures line-of-sight cluster velocities with
normal errors of 100 km/s for all clusters with masses larger than $10^{14}$
solar masses over a sky area of up to 5000 square degrees. A simple Fisher
matrix analysis of this survey shows that the normalization of the matter power
spectrum and the dark energy equation of state can be constrained to better
than 10 percent, and the Hubble constant and the primordial power spectrum
index can be constrained to a few percent, independent of any other
cosmological observations. We also find that the current constraint on the
power spectrum normalization can be improved by more than a factor of two using
data from a 400 square degree survey and WMAP third-year priors. We also show
how the constraints on cosmological parameters changes if cluster velocities
are measured with normal errors of 300 km/s.
