Fix an odd prime p. For an imaginary quadratic field K, let G_K be the Galois group over K of its maximal unramified p-extension. In the 1980s, Cohen and Lenstra developed a heuristic which "explains" much about the variation of p-class groups of imaginary quadratic fields. By class field theory, the maximal abelian quotient of G_K is isomorphic to the p-class group of K, so it's natural to wonder about the distribution of the fundamental groups G_K. In joint work with Nigel Boston and Michael Bush, we formulate a heuristic of Cohen-Lenstra type for the variation of G_K based on a group-theoretical investigation. I will describe the rationale for the heuristic and present some numerical data in support of it.