The assumption for the last third of a century that stem cell-driven hematolymphopoietic chimerism was irrelevant to successful conventional whole organ transplantation has prompted alternative inadequate explanations of organ allograft acceptance. This assumption clouded the biologic meaning of successful organ as well as bone marrow transplantation, and precluded the development of a cardinal principle that accommodated all facets of transplantation. Recognition of this error and the incorporation of the chimerism factor into a two-way paradigm have allowed previous enigmas of organ as well as bone marrow engraftment to be explained. No credible evidence has emerged to interdict this interactive concept. If the two-way paradigm is correct, it will allow the remarkable advances that have been made in basic immunology to be more meaningfully exploited for transplantation, including that of xenografts.