Using techniques from the theory of topological Ramsey spaces, we prove a dual Ramsey theorem for countable ordinals. Specifically, for each countable ordinal $\alpha$ we define a topological Ramsey space of equivalence relations on $\omega$ which code equivalence relations on $\alpha$, up to a necessary restriction on the set of minimal representatives of the equivalence classes. This extends the classical dual Ramsey theorem of Carlson and Simpson. This is joint work with Stevo Todorcevic.