The first observation of a parity-violation effect in molecules induced by weak interactions is still a dream that requires the synthesis and, eventually, the resolution of the enantiomers of well-chosen simple chiral molecules together with an appropriate experimental set-up for high-resolution spectroscopy. Performing IR spectroscopy on highly enantiomerically enriched samples of bromochlorofluoromethane succeeded in giving an upper limit of 10(-13) for the relative vibrational energy difference between the two enantiomers. These results led us to conceive a new experimental set-up based on a supersonic molecular beam and to work on other chiral molecules, such as chlorofluoroiodomethane. A synthesis of (+/-)-CHCIFI from racemic chlorofluoroiodoacetic acid should, in the near future permit the preparation of optically active samples of this haloform. The development of molecular beam spectroscopy using a two-photon Ramsey-fringes experiment should allow us to reach the precision needed to observe parity violation. These experimental challenges, which stimulate a close collaboration between chemists and physicists, are presented. The success of these projects would open the route to new information on the molecular Hamiltonian, a better knowledge of the electroweak interaction, and a better control of the various chirality-related properties of simple molecules.