We have measured the CP asymmetry A(CP) identical with[gamma(b-->sgamma)-gammab-->sgamma)]/[gamma(b-->sgamma)+gamma(b-->sgamma)] to be A(CP) = (-0.079+/-0.108+/-0.022) (1.0+/-0.030), implying that, at 90% confidence level, A(CP) lies between -0.27 and +0.10. These limits rule out some extreme non-standard-model predictions, but are consistent with most, as well as with the standard model.