  We present a method for determining the rms mass fluctuations on 8 h^-1 Mpc
scale, sigma8. The method utilizes the rate of evolution of the abundance of
rich clusters of galaxies. Using the Press-Schechter approximation, we show
that the cluster abundance evolution is a strong function of sigma8: d log n/dz
~ -1/sigma8^2; low sigma8 models evolve exponentially faster than high sigma8
models, for a given mass cluster. For example, the number density of Coma-like
clusters decreases by a factor of ~10^3$ from z = 0 to z ~ 0.5 for sigma8=0.5
models, while the decrease is only a factor of ~5 for sigma8 ~ 1. The strong
exponential dependence on sigma8 arises because clusters represent rarer
density peaks in low sigma8 models. We show that the evolution rate at z < 1 is
insensitive to the density parameter $\Omega$ or to the exact shape of the
power spectrum. Cluster evolution therefore provides a powerful constraint on
sigma8. Using available cluster data to z ~ 0.8, we find sigma8 = 0.83 +/-
0.15. This amplitude implies a bias parameter b ~ 1/sigma8 = 1.2 +/- 0.2, i.e.,
a nearly unbiased universe with mass approximately tracing light on large
scales.
