In this paper we propose a game theoretic approach to the allocation of channels to multiple cognitive users who share a set of frequencies. The famous Gale-Shapley stable matching algorithm is utilized to compute the channel allocations. We analyze the stable matching performance for the case of cognitive resource allocation and prove that in contrast to the general case, in the cognitive resource allocation problem there is a unique stable matching. We then show that the stable matching has performance very close to the optimal centralized allocation. It always achieves at least half of the total rate of the centralized allocation and under Rayleigh fading it achieves about 96% of the total centralized rate. Comparisons to random channel allocations are also discussed.