  We have studied the rare weak radiative hyperon decay Cascade0-->Sigma0/gamma
in the KTeV experiment at Fermilab. We have identified 4045 signal events over
a background of 804 events. The dominant Cascade0-->Lambda/pi0 decay, which was
used for normalization, is the only important background source. An analysis of
the acceptance of both modes yields a branching ratio of
BR(Cascade0-->Sigma0/gamma)=(3.34 +/- 0.05 +/- 0.09) x 10^(-3). By analyzing
the final state decay distributions, we have also determined that the Sigma0
emission asymmetry parameter for this decay is alpha = -0.63 +/- 0.09.
