A new class of non-Gaussian curvature fluctuations \zeta_{pr} (\bx) \equiv \delta N(\chi_i) arises from the post-inflation preheating behaviour of a non-inflaton field \chi_i. Its billiard-like chaotic dynamics imprints regular log-spaced narrow spikes in the number of preheating e-folds N(\chi_i). We perform highly accurate lattice simulations of SUSY-inspired quartic inflaton and coupling potentials in a separate-universe approximation to compute N(\chi_i) as a function of the (nearly homogeneous) initial condition \chi_i. The super-horizon modes of \chi_i(\bx) result in positive spiky excursions in \zeta_{pr} and hence negative gravitational potential fluctuations added to the usual sign-independent inflaton-induced perturbations, observably manifested in large cosmic structures and as (polarized) temperature CMB cold spots.