Humans routinely communicate to coordinate their activities, persisting and elaborating signals to pursue goals that cannot be accomplished individually. Communicative persistence is associated with complex cognitive skills such as intentionality, because interactants modify their communication in response to another's understanding of their meaning. Here we show that two language-trained chimpanzees effectively use intentional gestures to coordinate with an experimentally naive human to retrieve hidden food, providing some of the most compelling evidence to date for the role of communicative flexibility in successful coordination in nonhumans. Both chimpanzees (named Panzee and Sherman) increase the rate of non-indicative gestures when the experimenter approaches the location of the hidden food. Panzee also elaborates her gestures in relation to the experimenter's pointing, which enables her to find food more effectively than Sherman. Communicative persistence facilitates effective communication during behavioural coordination and is likely to have been important in shaping language evolution.