We study a model where rational agents act sequentially in a predetermined order, observing the actions chosen by their predecessors and then selecting an action. Agents engage in costly search to learn about the quality of various actions. Search costs of agents are private to them, and are independently and identically distributed across agents. We show that asymptotic learning, i.e, that late moving agents always select the optimal action, occurs if and only if search costs are not bounded away from zero. We explicitly characterize “common search order equilibria” in which agents choose to search in the same order.