  Variations in $\Omega$, the total density of the Universe, leave a clear and
distinctive imprint on the power spectrum of temperature fluctuations in the
cosmic microwave background (CMB). This signature is virtually independent of
other cosmological parameters or details of particular cosmological models. We
evaluate the precision with which $\Omega$ can be determined by a CMB map as a
function of sky coverage, pixel noise, and beam size. For example, assuming
only that the primordial density perturbations were adiabatic and with no prior
information on the values of any other cosmological parameters, a full-sky CMB
map at $0.5^\circ$ angular resolution and a noise level of $15\,\mu{\rm K}$ per
pixel can determine $\Omega$ with a variance of 5\%. If all other cosmological
parameters are fixed, $\Omega$ can be measured to better than 1\%.
