  The weak interaction does not conserve parity and therefore induces energy
shifts in chiral enantiomers that should in principle be detectable in
molecular spectra. Unfortunately, the magnitude of the expected shifts are
small and in spectra of a mixture of enantiomers, the energy shifts are not
resolvable. We propose a nuclear magnetic resonance (NMR) experiment in which
we titrate the chirality (enantiomeric excess) of a solvent and measure the
diasteriomeric splitting in the spectra of a chiral solute in order to search
for an anomalous offset due to parity nonconservation (PNC). We present a
proof-of-principle experiment in which we search for PNC in the
\textsuperscript{13}C resonances of small molecules, and use the
\textsuperscript{1}H resonances, which are insensitive to PNC, as an internal
reference. We set a new constraint on molecular PNC in \textsuperscript{13}C
chemical shifts at a level of $10^{-5}$\,ppm, and provide a discussion of
important considerations in the search for molecular PNC using NMR
spectroscopy.
