  We introduce and study the distribution of an estimator for the normalized
bispectrum of the Cosmic Microwave Background (CMB) anisotropy. We use it to
construct a goodness of fit statistic to test the coadded 53 and 90 GHz
COBE-DMR 4 year maps for non-Gaussianity. Our results indicate that Gaussianity
is ruled out at the confidence level in excess of 98%. This value is a lower
bound, given all the investigated systematics. The dominant non-Gaussian
contribution is found near the multipole of order $\ell=16$. Our attempts to
explain this effect as caused by the diffuse foreground emission from the
Galaxy have failed. We conclude that unless there exists a microwave foreground
emission which spatially correlates neither with the DIRBE nor Haslam maps, the
cosmological CMB anisotropy is genuinely non-Gaussian.
