We introduce and study the distribution of an estimator for the normalized
bispectrum of the cosmic microwave background (CMB) anisotropy. We use it t
o construct a goodness-of-fit statistic to test the co-added 53 and 90 GHz
COBE Diffuse Microwave Radiometer 4 year maps for non-Gaussianity. Our resu
lts indicate that Gaussianity is ruled out at the confidence level in exces
s of 98%. This value is a lower bound, given all the investigated systemati
cs. The dominant non-Gaussian contribution is found near the multipole of o
rder l = 16. Our attempts to explain this effect as caused by the diffuse f
oreground emission from the Galaxy have failed. We conclude that unless the
re exists a microwave foreground emission that spatially correlates with ne
ither the DIRBE nor Haslam maps, the cosmological CMB anisotropy is genuine
ly non-Gaussian.