Large fluctuations of conductivity with time are observed in a low-mobility two-dimensional electron system in silicon at low electron densities $n_s$ and temperatures. A dramatic increase of the noise power ($propto 1/f^{alpha}$) as $n_s$ is reduced below a certain density $n_g$, and a sharp jump of $alpha$ at $n_sapprox n_g$, are attributed to the freezing of the electron glass at $n_s = n_g$. The data strongly suggest that glassy dynamics persists in the metallic phase.