We study the production of fermions through a derivative coupling to an axion inflaton and the effects of the produced fermions on the scalar and tensor metric perturbations. We show how such a coupling can arise naturally from supergravity with an axion-like field driving large-field inflation and small instanton-like corrections. We present analytic results for the scalar and tensor power spectra, and estimate the amplitude of the non-Gaussianties in the equilateral regime. The scalar spectrum is found to have a red-tilted spectral index, small non-Gaussianities, and can be dominant over the vacuum contribution. In contrast, the tensor power spectrum from the fermions is always subdominant compared to the vacuum contribution. The pseudoscalar coupling will favor production of one chirality of the fermions over the other, and therefore, it is expected that the resulting gravitational waves will be chiral. However, the parity-odd component of the power spectrum is shown to be subdominant to the parity-even component. The combined results of the scalar and tensor spectra allow to lower the energy scale of inflation, effectively lowering the tensor-to-scalar ratio. Chaotic inflation, in which the inflationary potential is quadratic, is currently ruled out as it predicts too large a tensor-to-scalar ratio. We show how this fermion-axion model can allow for quadratic inflation which agrees with all current measurements.