Let J(2k,k) be the Johnson graph whose vertices are the k-subsets of a 2k-element set, with two vertices adjacent when their intersection has size k-1. Let theta(G) be the minimum number of cliques whose vertex sets cover V(G). For which positive integers k does theta(J(2k,k)) equal the k-th Catalan number C_k? In particular, does equality hold for every even k?