<p>Cosmological correlation functions of inflaton and graviton perturbations are the fundamental observables of early universe cosmology and remain a primary target for observations. In this work, we ask the following question: are these observables independent of one another? We find that in the parity-odd sector of inflationary perturbation theory, the answer is a resounding no! In earlier work we derived a <i>correlator-to-correlator</i> factorisation formula which states that parity-odd correlators factorise into lower-point correlators under some mild assumptions on the underlying theory. In this work, we show that these assumptions are satisfied in <i>dynamical Chern-Simons gravity</i> where the action of minimal inflation is augmented by a coupling between the inflaton and the gravitational Chern-Simons term. Such a theory gives rise to a parity-odd trispectrum of curvature perturbations, and we show that such a trispectrum can be expressed solely in terms of the bispectrum that arises due to the minimal coupling between the inflaton and graviton, and the graviton power spectrum which receives a parity-odd correction in this theory. The trispectrum is quadratic in this mixed inflaton-graviton bispectrum and can therefore be interpreted as a “double copy”. Our final expression for the parity-odd trispectrum is a relatively simple function of the external momenta that is rational and factorised.</p>