We prove that three-dimensional N=1 supersymmetric Yang-Mills-Chem-Sim
ons theory is finite to all loop orders, In general this leaves open t
he possibility that different regularization methods lead to different
finite effective actions. We show that in this model dimensional regu
larization and regularization by dimensional reduction yield the same
effective action. Consequently, the superfield approach preserves BRS
invariance for this model.