Allelopathy is the chemical inhibition of one species by another. Bacteriocins, which are toxins produced by bacteria to inhibit the growth of closely related species, are a particular type of allelopathy that is of special interest because of the importance of bacteriocins in the food industry and in the development of vaccines. We form a model of this situation in the chemostat by incorporating parameters that measure relatedness and mutation rates as well as the cost of toxin production into standard competition models. Numerically, we show that depending upon growth rates and toxin sensitivity, coexistence of competitors may or may not occur.