We consider contributions to non-Gaussianity of the cosmic microwave background (CMB) from remnants of phase transitions in the very early Universe. Such signatures can optimistically be used to discover evidence of new particle physics through cosmological observations. More conservatively they may provide an obstacle to extracting information about the non-Gaussian nature of primordial density fluctuations from any detection in the CMB. We study this explicitly by computing the bispectrum from global textures, which occur in a wide class of particle physics models.