The ability to differentiate chiral molecules of different handedness is of great importance for chemical and life sciences. Since most of the relevant chiral molecules have their chiral transitions in the UV region, detecting their circular dichroism (CD) signal is associated with practical experimental challenges of performing optical measurements in that spectral range. To address this problem, here, we study the possibility of shifting CD signal of a model chiral medium 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\'erot microcavity one can imprint the hybrid mode splitting, the hallmark of strongly coupled systems, on the CD spectrum of the coupled system and thereby effectively shift the chiral resonance of the model system to lower energies. We first predict the effect using analytical transfer-matrix method as well as numerical finite-difference time-domain (FDTD) simulations. Furthermore, we confirm the validity of theoretical predictions in a proof-of-principle experiment involving chiral plasmonic nanoparticles coupled to a Fabry-P\'erot microcavity.
