The development of the unique, hierarchical, and endless combinatorial capacity in a human language requires neural maturation and learning through childhood. Compared with most non-human primates, where combinatorial capacity seems limited, chimpanzees present a complex vocal system comprising hundreds of vocal sequences. We investigated how such a complex vocal system develops and the processes involved. We recorded 10,929 vocal utterances of 98 wild chimpanzees aged 0-55 years, from Taï National Park, Ivory Coast. We developed customized Generalized non-Linear Models to estimate the ontogenetic trajectory of four structural components of vocal complexity: utterance length, diversity, probability of panting (requiring phonation across inhalation and exhalation), and probability of producing two adjacent panted units. We found chimpanzees need 10 years to reach adult levels of vocal complexity. In three variables, the steepest increase coincided with the age of first non-kin social interactions (2-5 years), and plateaued in sub-adults (8-10 years), as individuals integrate into adult social life. Producing two adjacent panted units may require more neuromuscular coordination of the articulators, as its emergence and steepest increase appear later in development. These results suggest prolonged maturational processes beyond those hitherto thought likely in species that do not learn their vocal repertoire. Our results suggest that multifaceted ontogenetic processes drive increases in vocal structural complexity in chimpanzees, particularly increases in social complexity and neuro-muscular maturation. As humans live in a complex social world, empirical support for the "social complexity hypothesis" may have relevance for theories of language evolution. RESEARCH HIGHLIGHTS: Chimpanzees need around 10 years to develop the vocal structural complexity present in the adult repertoire, way beyond the age of emergence of every single vocal unit. Multifaceted ontogenetic processes may drive increases in vocal structural complexity in chimpanzees, particularly increases in social complexity and neuro-muscular maturation. Non-linear increases in vocal complexity coincide with social developmental milestones. Vocal sequences requiring rapid articulatory change emerge later than other vocal sequences, suggesting neuro-muscular maturational processes continue through the juvenile years.