We study the time evolution from a pure state with extensive energy above the ground state in a CFT. We show that the reduced density matrix of an interval of length ℓ in an infinite system is exponentially close to a thermal one after times t>ℓ/2. For a finite system of length L we study the overlap of the state at time t with the initial state and show that this can expressed in terms of Virasoro characters. For a rational CFT there are finite revivals when t is a multiple of L/2, and interesting structure near all rational values of t/L. We also study the effect of an irrelevant operator which breaks the integrability and show that the revivals then become increasingly broadened.