The hierarchical organization of sequential behaviour, and the ability to compensate for nonadjacent sequential dependencies, are fundamental and interrelated abilities supporting complex human behaviours, including language and tool use. To understand how the cognition underlying these structural properties of human behaviour 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. However thus far, evidence supporting this hypothesis 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 organized during tool use. Half of adult chimpanzees produce nonadjacent dependencies at significantly greater sequential distances than comparable, nonhierarchical Markov models, including when 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 most chimpanzees draw upon forms of hierarchical structuring when organizing behaviours during tool use. Our analysis offered the greatest support for a system of organization which involved the production of short subroutines of actions (2 to 8 actions), which are hierarchically arranged into sequences, and is consistent with previous qualitative descriptions of ape tool-use behaviours. Interindividual variability was detected within our analysis in both the 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 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.