We introduce and theoretically analyze the concept of manipulating optical chirality via strong coupling of the optical modes of chiral nanostructures with excitonic transitions in molecular layers or semiconductors. With chirality being omnipresent in chemistry and biomedicine, and highly desirable for technological applications related to efficient light manipulation, the design of nanophotonic architectures that sense the handedness of molecules or generate the desired light polarization in an externally controllable manner is of major interdisciplinary importance. Here we propose that such capabilities can be provided by the mode splitting resulting from polaritonic hybridization. Starting with an object with well-known chiroptical response-here, for a proof of concept, a chiral sphere-we show that strong coupling with a nearby excitonic material generates two spectral branches that retain the object's high chirality density, which manifest most clearly through anticrossings in circular-dichroism or differential-scattering dispersion diagrams. These windows can be controlled by the intrinsic properties of the excitonic layer and the strength of the interaction, enabling thus the post-fabrication manipulation of optical chirality. Our findings are further verified via simulations of circular dichroism of a realistic chiral architecture, namely a helical assembly of plasmonic nanospheres embedded in a resonant matrix.