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Résumé : Abstract Cosmological correlators from inflation are often generated at tree level and hence loop contributions are bounded to be small corrections by perturbativity. Here we discuss a scenario where this is not the case. Recently, it has been shown that for any number of scalar fields of any mass, the parity-odd trispectrum of a massless scalar must vanish in the limit of exact scale invariance due to unitarity and the choice of initial state. By carefully handling UV-divergences, we show that the one-loop contribution is non-vanishing and hence leading. Surprisingly, the one-loop parity-odd trispectrum is simply a rational function of kinematics, which we compute explicitly in a series of models, including single-clock inflation. Although the loop contribution is the leading term in the parity-odd sector, its signal-to-noise ratio is typically bounded from above by that of a corresponding tree-level parity-even trispectrum, unless instrumental noise and systematics for the two observables differ. Furthermore, we identify a series of loop contributions to the wavefunction that cancel exactly when computing correlators, suggesting a more general phenomenon.