A vital prerequisite for cumulative culture, a phenomenon often asserted to be unique to humans, is the ability to modify behaviour and flexibly switch to more productive or efficient alternatives. Here, we first established an inefficient solution to a foraging task in five captive chimpanzee groups (N = 19). Three groups subsequently witnessed a conspecific using an alternative, more efficient, solution. When participants could successfully forage with their established behaviours, most individuals did not switch to this more efficient technique; however, when their foraging method became substantially less efficient, nine chimpanzees with socially-acquired information (four of whom witnessed additional human demonstrations) relinquished their old behaviour in favour of the more efficient one. Only a single chimpanzee in control groups, who had not witnessed a knowledgeable model, discovered this. Individuals who switched were later able to combine components of their two learned techniques to produce a more efficient solution than their extensively used, original foraging method. These results suggest that, although chimpanzees show a considerable degree of conservatism, they also have an ability to combine independent behaviours to produce efficient compound action sequences; one of the foundational abilities (or candidate mechanisms) for human cumulative culture.