There is increasing evidence for cultural variations in behaviour among non-human species, but human societies additionally display elaborate cumulative cultural evolution, with successive generations building on earlier achievements. Evidence for cumulative culture in non-human species remains minimal and controversial. Relevant experiments are also lacking. Here we present a first experiment designed to examine chimpanzees' capacity for cumulative social learning. Eleven young chimpanzees were presented with a foraging device, which afforded both a relatively simple and a more complex tool-use technique for extracting honey. The more complex 'probing' technique incorporated the core actions of the simpler 'dipping' one and was also much more productive. In a baseline, exploration condition only two subjects discovered the dipping technique and a solitary instance of probing occurred. Demonstrations of dipping by a familiar human were followed by acquisition of this technique by the five subjects aged three years or above, whilst younger subjects showed a significant increase only in the elements of the dipping technique. By contrast, subsequent demonstrations of the probing task were not followed by acquisition of this more productive technique. Subjects stuck to their habitual dipping method despite an escalating series of demonstrations eventually exceeding 200. Supplementary tests showed this technique is within the capability of chimpanzees of this age. We therefore tentatively conclude that young chimpanzees exhibit a tendency to become 'stuck' on a technique they initially learn, inhibiting cumulative social learning and possibly constraining the species' capacity for cumulative cultural evolution.