  We search the high-latitude portion of the COBE Differential Microwave
Radiometers (DMR) 4-year sky maps for evidence of a non-Gaussian temperature
distribution in the cosmic microwave background. The genus, 3-point correlation
function, and 2-point correlation function of temperature maxima and minima are
all in excellent agreement with the hypothesis that the CMB anisotropy on
angular scales of 7 degrees or larger represents a random-phase Gaussian field.
A likelihood comparison of the DMR sky maps to a set of random-phase
non-Gaussian toy models selects the exact Gaussian model as most likely. Monte
Carlo simulations show that the 2-point correlation of the peaks and valleys in
the maps provides the greatest discrimination among the class of models tested.
