How are the class groups of imaginary quadratic fields distributed? The Cohen-Lenstra heuristics give a conjectural answer to this question based on objects appearing inversely proportionally often to their number of automorphisms. We consider the generalization of this question where we replace imaginary quadratic fields with any kind of number field, and we replace the class group with its non-abelian analog, the Galois group of the maximal unramified extension. We give a simple heuristic to predict the distribution of these unramified Galois groups and explain that on the abelianization (class group) our heuristic is equivalent to heuristics of Cohen, Lenstra, and Martinet. Finally, we give a theorem proving the predictions of this heuristic for function fields over finite fields $\mathbb{F}_q$, when $q$ is taken to infinity.