The transmission of a homogeneously aligned chiral smectic A liquid crystal, placed between crossed and parallel polarizers, is measured as a function of polarization angle for a series of applied voltages. The experimental results exhibit a pronounced field-dependent birefringence, providing clear evidence for field-induced biaxiality in the refractive index in these systems. It is shown that the biaxiality is strongly correlated with the electroclinic tilt angle.