Potential advantages of chiral molecules for a sensitive search for parity violating cosmic fields are highlighted. Such fields are invoked in different models for cold dark matter or in the Lorentz-invariance violating standard model extensions and thus are signatures of physics beyond the standard model. The sensitivity of a 20-year-old experiment with the molecule CHBrClF to pseudovector cosmic fields as characterized by the parameter |b_{0}^{e}| is estimated to be O(10^{-12} GeV) employing ab initio calculations. This allows us to project the sensitivity of future experiments with favorable choices of chiral heavy-elemental molecular probes to be O(10^{-17} GeV), which will be an improvement of the present best limits by at least two orders of magnitude.