The Standard Model violates parity, but only by mechanisms which are invisible to Large Hadron Collider (LHC) experiments (on account of the lack of initial state polarisation or spin-sensitivity in the detectors). Nonetheless, new physical processes could potentially violate parity in ways which are detectable by those same experiments. If those sources of new physics occur only at LHC energies, they are untested by direct searches. We probe the feasibility of such measurements using approximately 0.2 inverse femtobarns of data which was recorded in 2012 by the CMS collaboration and made public within the CMS Open Data initiative. In particular, we test an inclusive three-jet event selection which is primarily sensitive to non-standard parity violating effects in quark-gluon interactions. Within our measurements, no significant deviation from the Standard Model is seen and no obvious experimental limitations have been found. We discuss other ways that searches for non-standard parity violation could be performed, noting that these would be sensitive to very different sorts of models to those which our measurements constrain. We hope that our initial studies provide a valuable starting point for rigorous future analyses using the full LHC datasets at 13 TeV with a careful and less conservative estimate of experimental uncertainties.