  We use the two-point correlation function of the extrema points (peaks and
valleys) in the COBE Differential Microwave Radiometers (DMR) 2-year sky maps
as a test for non-Gaussian temperature distribution in the cosmic microwave
background anisotropy. A maximum likelihood analysis compares the DMR data to
n=1 toy models whose random-phase spherical harmonic components $a_{\ell m}$
are drawn from either Gaussian, $\chi^2$, or log-normal parent populations. The
likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model.
All non-Gaussian models tested are ruled out at 90\% confidence, limited by
type II errors in the statistical inference. The extrema correlation function
is a stronger test for this class of non-Gaussian models than topological
statistics such as the genus.
