  An old problem of Erd\H{o}s, Fajtlowicz and Staton asks for the order of a
largest induced regular subgraph that can be found in every graph on n
vertices. Motivated by this problem, we consider the order of such a subgraph
in a typical graph on n vertices, i.e., in a binomial random graph G(n,1/2). We
prove that with high probability a largest induced regular subgraph of G(n,1/2)
has about n^{2/3} vertices.
