Many of the complex behaviours of humans involve the production of nonadjacent dependencies between sequence elements, which in part can be generated through the hierarchical organization of sequences. To understand how these structural properties of human behaviours evolved, we can gain valuable insight from studying the sequential behaviours of nonhuman animals. Among the behaviours of nonhuman apes, tool use has been hypothesised to be a domain of behaviour which likely involves hierarchical organization, and may therefore possess nonadjacent dependencies between sequential actions. However thus far, evidence supporting hierarchical organization of great-ape tool use comes from methodologies which have been criticised in their objectivity. Additionally, the extent to which nonadjacent dependencies appear in primate action sequences during tool use has not been formally investigated. We used estimations of mutual information (MI)-a measure of dependency strength between sequence elements-to evaluate both the extent to which wild chimpanzees produce nonadjacent dependencies during a naturalistic tool-use task (nut cracking), as well as how sequences of actions are likely organized during tool use. Half of adult chimpanzees produced nonadjacent dependencies at significantly greater sequential distances than comparable, nonhierarchical Markov models once repeated actions had been accounted for. Additionally, for the majority of chimpanzees, MI decay with increasing sequential distance included a power-law relationship, which is a key indicator that the action sequences produced by chimpanzees likely entail some degree of hierarchical organization. Our analysis offered the greatest support for a system of organization where short subroutines of actions (2-8 actions long) are hierarchically arranged into longer sequences-a finding which is consistent with previous qualitative descriptions of ape tool-use behaviours. Interindividual variability was detected within our analysis in both the maximum distance dependencies were detected, and the most likely structuring mechanism for sequential action organization. We discuss these results in light of possible interindividual variation in the systems of action organization used by chimpanzees during tool use, in addition to methodological considerations for applications of MI estimations to sequential behaviours. Moreover, we discuss our main findings alongside hypotheses for the coevolution of complex syntax in language and tool-action across hominin evolutionary history.