In this report, we propose a novel mathematical model of the origin and evolution of sex determination in vertebrates that is based on the stochastic epigenetic modification (SEM) mechanism. We have previously shown that SEM, with rates consistent with experimental observation, can both increase the rate of gene fixation and decrease pseudogenization, thus dramatically improving the efficacy of evolution. Here, we present a conjectural model of the origin and evolution of sex determination wherein the SEM mechanism alone is sufficient to parsimoniously trigger and guide the evolution of heteromorphic sex chromosomes from the initial homomorphic chromosome configuration, without presupposing any allele frequency differences. Under this theoretical model, the SEM mechanism (i) predated vertebrate sex determination origins and evolution, (ii) has been conveniently and parsimoniously co-opted by the vertebrate sex determination systems during the evolutionary transitioning to the extant vertebrate sex determination, likely acting "on top" of these systems, and (iii) continues existing, alongside all known vertebrate sex determination systems, as a universal pan-vertebrate sex determination modulation mechanism.