Chirality plays a fundamental part in the activity of biological molecules and broad classes of chemical reactions, but detecting and quantifying it remains challenging. The spectroscopic methods of choice are usually circular dichroism and vibrational circular dichroism, methods that are forbidden in the electric dipole approximation. The resultant weak effects produce weak signals, and thus require high sample densities. In contrast, nonlinear techniques probing electric-dipole-allowed effects have been used for sensitive chiral analyses of liquid samples. Here we extend this class of approaches by carrying out nonlinear resonant phase-sensitive microwave spectroscopy of gas phase samples in the presence of an adiabatically switched non-resonant orthogonal electric field; we use this technique to map the enantiomer-dependent sign of an electric dipole Rabi frequency onto the phase of emitted microwave radiation. We outline theoretically how this results in a sensitive and species-selective method for determining the chirality of cold gas-phase molecules, and implement it experimentally to distinguish between the S and R enantiomers of 1,2-propanediol and their racemic mixture. This technique produces a large and definitive signature of chirality, and has the potential to determine the chirality of multiple species in a mixture.