  We compute the three-point temperature correlation function of the {\it COBE}
Differential Microwave Radiometer (DMR) first-year sky maps to search for
non-Gaussian temperature fluctuations. The level of fluctuations seen in the
computed correlation function are too large to be attributable solely to
instrument noise. However the fluctuations are consistent with the level
expected to result from a superposition of instrument noise and sky signal
arising from a Gaussian power law model of initial fluctuations, with a
quadrupole normalized amplitude of 17 $\mu$K and a power law spectral index $n
= 1$. We place limits on the amplitude of intrinsic three-point correlations
with a variety of predicted functional forms.
