Let K be a finitely-generated field of characteristic zero, and let f(x) and u(x) be rational functions of degree at least 2 with coefficients in K. I will show that, for any P in K, the set {n in N: f^n(P) is in u(K)} is the union of finitely many one-sided arithmetic progressions. This resolves a conjecture of Cahn, Jones and Spear, and may be viewed as either an arithmetic-dynamical analogue of the Mordell-Lang conjecture or an arithmetic analogue of the dynamical Mordell-Lang conjecture.