We introduce a novel configuration for the broadband measurement of the optical activity of molecules, combining time-domain detection with heterodyne amplification. A birefringent common-path polarization-division interferometer creates two phase-locked replicas of the input light with orthogonal polarization. The more intense replica interacts with the sample, producing a chiral free-induction decay field, which interferes with the other replica, acting as a time-delayed phase-coherent local oscillator. By recording the delay-dependent interferogram, we obtain by a Fourier transform both the circular dichroism and circular birefringence spectra. Our compact, low-cost setup accepts ultrashort light pulses, making it suitable for measurement of transient optical activity.