  COBE has provided us with a whole-sky map of the CBR anisotropies. However,
even if the noise level is negligible when the four year COBE data are
available, the cosmic variance will prevent us from obtaining information about
the Gaussian nature of the primordial fluctuations. This important issue is
addressed here by studying the angular bispectrum of the cosmic microwave
background anisotropies. A general form of the angular bispectrum is given and
the cosmic variance of the angular bispectrum for Gaussian fluctuations is
calculated. The advantage of using the angular bispectrum is that one can
choose to use the multipole moments which minimize the cosmic variance term.
The non-Gaussian signals in most physically motivated non-Gaussian models are
small compared with cosmic variance. Unless the amplitudes are large, the
non-Gaussian signals are only detectable in the COBE data in those models where
the angular bispectrum is flat or increases with increasing multipole moment.
