Geometrical chirality is a widespread phenomenon that has fundamental implications for discriminating enantiomers of biomolecules. In order to enhance the chiral response of the medium, it has been suggested to couple chiral molecules to resonant optical cavities in order to enhance the circular dichroism (CD) signal at the resonant frequency of the cavity. Here, we studied a distinctly different regime of chiral light-matter interaction, wherein the CD signal of a chiral medium splits into polaritonic modes by reaching the strong coupling regime with an optical microcavity. Specifically, we show that by strongly coupling chiral plasmonic nanoparticles to a non-chiral Fabry-P\ue9rot microcavity one can imprint the mode splitting on the CD spectrum of the coupled system and thereby effectively shift the initial chiral resonance to a different energy. We first examined the effect with the use of analytical transfer-matrix method as well as numerical finite-difference time-domain (FDTD) simulations. Furthermore, we confirmed the validity of theoretical predictions in a proof-of-principle experiment involving chiral plasmonic nanoparticles coupled to a Fabry-P\ue9rot microcavity
