With a crystallographic root system Φ, there are associated two Catalan objects, the set of nonnesting partitions NN(Φ), and the cluster complex ∆(Φ). These possess a number of enumerative coincidences, many of which are captured in a surprising identity, first conjectured by Chapoton. We prove this conjecture, and indicate its generalisation for the Fuß-Catalan objects NN (Φ) and ∆(Φ), conject...