We show how R parity can break spontaneosly as a result of radiative corrections in unified N=1 supergravity models. We illustrate this with a concrete rank-four unified model, where the spontaneous breaking of R parity is accompanied by the existence of a physical Majoron. We determine the resulting supersymmetric particle mass spectrum and show that R-parity-breaking signals may be detectable at CERN LEP 200.