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Structure in the Universe is widely believed to have originated from quantum fluctuations during an early epoch of accelerated expansion. Yet, the patterns we observe today do not distinguish between quantum or classical primordial fluctuations; current cosmological data is consistent with either possibility. We argue here that a detection of primordial non-Gaussianity can resolve the present situation, and provide a litmus-test for the quantum origin of cosmic structure. Unlike in quantum mechanics, vacuum fluctuations cannot arise in classical theories and therefore long-range classical correlations must result from (real) particles in the initial state. Similarly to flat-space scattering processes, we show how basic principles require these particles to manifest themselves as poles in the $n$-point functions, in the so-called folded configurations. Following this observation, and assuming fluctuations are (i) correlated over large scales, and (ii) generated by local evolution during an inflationary phase, we demonstrate that: the absence of a pole in the folded limit of non-Gaussian correlators uniquely identifies the quantum vacuum as the initial state. In the same spirit as Bell's inequalities, we discuss how this can be circumvented if locality is abandoned. We also briefly discuss the implications for simulations of a non-Gaussian universe.