  We show that theories of inflation with multiple, rapidly turning fields can
generate large amounts of non-Gaussianity. We consider a general theory with
two fields, an arbitrary field-space metric, and a potential that supports
sustained, rapidly turning field trajectories. Our analysis accounts for
non-zero field cross-correlation and does not fix the power spectra of
curvature and isocurvature perturbations to be equal at horizon crossing. Using
the $\delta N$ formalism, we derive a novel, analytical formula for bispectrum
generated from multi-field mixing on super-horizon scales. Rapid-turn inflation
can produce a bispectrum with several potentially large contributions that are
not necessarily of the local shape. We exemplify the applicability of our
formula with a fully explicit model and show that the new contributions indeed
can generate a large amplitude of local non-Gaussianity, $f_{\rm NL}^{\rm
loc}\sim {\cal O}(1)$. These results will be important when interpreting the
outcomes of future observations.
