Using an analytical model for the Cosmic Microwave Background anisotropies
produced by textures, we compute the resulting collapsed three--point
correlation function and the {\it rms} expected value due to the cosmic
variance. We apply our calculations to the {\sl COBE}--DMR experiment and test
the consistency of the model with the observational results. We also show that
an experiment with smaller angular resolution can put bounds to the model
parameters.Comment: 13 pp, RevTeX, 4 PostScript figures, to appear in Phys.Rev.