A central goal in ecology is to understand the mechanisms by which biological diversity is maintained. The diversity of plant chemical defences and the strategies by which they are deployed in nature may influence biological diversity. Trees in neotropical forests are subject to relatively high herbivore pressure. Such consistent pressure is thought to select for constitutive, non-flexible defence-related phytochemistry with limited capacity for inducible phytochemical responses. However, this has not been explored for volatile organic compounds (VOCs) that have a relatively low ratio of production costs to ecological benefits. To test this, I sampled VOCs emitted from canopy leaves of 10 phylogenetically diverse tree species (3 Magnoliids and 7 Rosids) in the Peruvian Amazon before and after induction with the phytohormone methyl jasmonate (MeJA). There was no phylogenetic signal in induction or magnitude of MeJA-induced VOC emissions from intact leaves: all trees induced VOC profiles dominated by β-ocimene, linalool, and α-farnesene of varying ratios. Moreover, overall inducibility of VOCs from intact leaves was unrelated to phytochemical diversity or richness. In contrast, experimentally wounded leaves showed considerable phylogeny-based and MeJA-independent variation the richness and diversity of constitutive wound-emitted VOCs. Moreover, VOC inducibility from wounded leaves correlated negatively with phytochemical richness and diversity, potentially indicating a tradeoff in constitutive and inducible defence strategies for non-volatile specialised metabolites but not for inducible VOCs. Importantly, there was no correlation between any chemical profile and either natural herbivory or leaf toughness. The coexistence of multiple phytochemical strategies in a hyper-diverse forest has broad implications for competitive and multitrophic interactions, and the evolutionary forces that maintain the exceptional plant biodiversity in neotropical forests.