  New sources of parity and time reversal violation are predicted by well
motivated extensions of the Standard Model and can be effectively probed by
precision spectroscopy of atoms and molecules. Chiral molecules have
distinguished enantiomers which are related by parity transformation. Thus,
they are promising candidates to search for parity violation at molecular
scales, yet to be observed. In this work, we show that precision spectroscopy
of the hyperfine structure of chiral molecules is sensitive to new physics
sources of parity and time reversal violation. In particular, such a study can
be sensitive to regions unexplored by terrestial experiments of a new chiral
spin-1 particle that couples to nucleons. We explore the potential to hunt for
time reversal violation in chiral molecules and show that it can be a
complementary measurement to other probes. We assess the feasibility of such
hyperfine metrology and project the sensitivity in CHDBrI$^+$.
