Prospective memory (PM) involves forming intentions, retaining those intentions, and later executing those intended responses at the appropriate time. Few studies have investigated this capacity in animals. Monkeys performed a computerized task that assessed their ability to remember to make a particular response if they observed a PM cue embedded within an ongoing learning-set (LS) task. At a break in the LS task, monkeys selected one of two icons indicating that they had or had not encoded the occurrence of the PM cue (the latter icon resumed the LS task). Critically, during this response period, the PM response icon appeared after a delay during which monkeys could self-initiate the PM response prior to receiving any external prompt. Monkeys selected the PM and LS icons when each was the optimal response, illustrating that they could encode, store, and respond appropriately to a stimulus event in the future. Critically, some monkeys self-initiated the PM response prior to that icon’s appearance, indicating that they could retrieve the PM and act on their intention to make that response without the aid of a prompt. These monkeys appeared capable of using PM in this task. Thus, this capacity appears not to be limited to humans.