  We propose a set of statistics $S_q$ for detecting non-gaussianity in CMBR
anisotropy data sets. These statistics are both simple and, according to
calculations over a space of linear combinations of three-point functions,
nearly optimal at detecting certain types of non-gaussian features. We apply
$S_3$ to the UCSB SP91 experiment and find that the mean of the four frequency
channels is by this criterion strongly non-gaussian. Such an observation would
be highly unlikely in a gaussian theory with a small coherence angle, such as
standard ($n=1$, $\Omega_b = .05$, $h = .5$) inflation. We cannot conclude that
the non-gaussianity is cosmological in origin, but if we assume it due instead
to foreground contamination or instrumental effects, and remove the points
which are clearly responsible for the non-gaussian behavior, the rms of the
remaining fluctuations is too small for consistency with standard inflation.
Further data are needed before definitive conclusions may be drawn. Finally, we
generalize the ideas behind this statistic to other types of non-gaussian
behavior that might be detected in other experimental schemes.
