The angle-resolved inner-shell photoionization of R-trifluoromethyloxirane, ${\mathrm{C}}_{3}{\mathrm{H}}_{3}{\mathrm{F}}_{3}\mathrm{O}$, is studied experimentally and theoretically. Thereby, we investigate the photoelectron circular dichroism (PECD) for nearly symmetric O $1s$ and F $1s$ electronic orbitals, which are localized on different molecular sites. The respective dichroic $\beta_{1}$ and angular distribution $\beta_{2}$ parameters are measured at the photoelectron kinetic energies from 1 to 16 eV by using variably polarized synchrotron radiation and velocity map imaging spectroscopy. The present experimental results are in good agreement with the outcome of ab initio electronic structure calculations. We report a sizable chiral asymmetry $\beta_{1}$ of up to about 9% for the $K$-shell photoionization of oxygen atom. For the individual fluorine atoms, the present calculations predict asymmetries of similar size. However, being averaged over all fluorine atoms, it drops down to about 2%, as also observed in the present experiment. Our study demonstrates a strong emitter and site sensitivity of PECD in the one-photon inner-shell ionization of this chiral molecule.