A Graded Autocatalysis Replication Domain (GARD) model is proposed, which provides a rigorous kinetic analysis of simple chemical sets that manifest mutual catalysis. It is shown that catalytic closure can sustain self-replication up to a critical dilution rate, λc, related to the graded extent of mutual catalysis. We explore the behavior of vesicles containing GARD species whose mutual catalysis is governed by a previously published statistical distribution. In the population thus generated, some GARD vesicles display a significantly higher replication efficiency than most others. GARD thus represents a simple model for primordial chemical selection of mutually catalytic sets.