Recent research has produced evidence for basic combinatorial abilities in the vocal systems of different animal species. Here, we investigate the structure of gesture sequences in Eastern chimpanzees (Pan troglodytes schweinfurthii) to detect whether gestural communication shows non-random combinations and how combinatorial rules influence predictability. Gesture, as compared to vocalization, offers greater flexibility in how signals are combined - for example overlapping in time - and as the parsing of signals into sequences is dependent on researcher decisions, we employ a multiverse approach, considering four different definitions of what constitutes a 'sequence' based on varying time thresholds. Our results indicate that sequences tend to be short (even with the most liberal time-window) and that transitions between some gesture types occur more frequently than expected by chance, with some transitions showing significant association across all time-windows. These transitions often involve repetition, suggesting persistence as a key aspect of chimpanzee gestural sequences. Information about previous gestures reduced uncertainty in predicting subsequent gestures. The order of gestures within sequences appears to be less critical than their cooccurrence, challenging assumptions based on the linear patterning derived from vocal communication. Our findings highlight the importance of methodological choices in sequence definition and suggest that chimpanzee gestural communication is characterised by a mix of predictability and flexibility, with implications for understanding the evolution of complex communication systems.