The random chemistry algorithm of Kauffman can be used to determine an unknown subset S of a fixed set V. The algorithm proceeds by zeroing in on S through a succession of nested subsets V=V_0,V_1,...,V_m=S. In Kauffmans original algorithm, the size
of each V_i is chosen to be half the size of V_{i-1}. In this paper we determine the optimal sequence of sizes so as to minimize the expected run time of the algorithm.
