A planar molecule may become chiral upon excitation of an out-of-plane vibration, changing its handedness during half a vibrational period. When exciting such a vibration in an ensemble of randomly oriented molecules with an infrared laser, half of the molecules will undergo the vibration phase-shifted by π compared to the other half, and no net chiral signal is observed. This symmetry can be broken by exciting the vibrational motion with a Raman transition in the presence of a static electric field. Subsequent ionization of the vibrating molecules by an extreme ultraviolet pulse probes the time-dependent net handedness via the photoelectron circular dichroism. Our proposal for pump-probe spectroscopy of molecular chirality, based on quantum-chemical theory and discussed for the example of the carbonyl chlorofluoride molecule, is feasible with current experimental technology.