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Realistic models of high-energy physics include multiple scalar fields. Renormalization requires that the fields have nonminimal couplings to the spacetime Ricci curvature scalar, and the couplings can be large at the energy scales of early-universe inflation. The nonminimal couplings induce a nontrivial field-space manifold in the Einstein frame, and they also yield an effective potential in the Einstein frame with nontrivial curvature. The ridges or bumps in the Einstein-frame potential can lead to primordial non-Gaussianities of observable magnitude. We develop a covariant formalism to study perturbations in such models and calculate the primordial bispectrum. As in previous studies of non-Gaussianities in multifield models, our results for the bispectrum depend sensitively on the fields’ initial conditions.