Consider a scenario where a source continuously monitors an object and sends time-stamped status updates to a destination through a rate-limited link. In order to measure the 'freshness' of the status information available at the destination, we adopt the metric called Age of Information (AoI). We assume all updates are of the same size, and arrive randomly at the source according to a Bernoulli process. Due to the link capacity constraint, it takes d(d< 2) time slots for the source to complete the transmission of an update. Therefore, when a new update arrives at the source during the transmission of another update, the source needs to decide whether to skip the new arrival or to switch to it, in order to minimize the expected average AoI at the destination. We prove that within a broadly defined class of online policies, the optimal policy should be a renewal policy, and has a sequential switching property. We then show that the optimal decision of the source in any time slot has a multiple-threshold structure, and only depends on the age of the update being transmitted and the AoI in the system. The thresholds are then numerically identified by formulating the problem as a Markov Decision Process (MDP).