The inner-shell photoionization of unoriented camphor molecules by circularly polarized light has been investigated from threshold to a photoelectron kinetic energy of approximately 65 eV. Photoelectron spectra of the carbonyl C 1s orbital, recorded at the magic angle of 54.7 degrees with respect to the light propagation direction, show an asymmetry of up to 6% on change of either the photon helicity or molecular enantiomer. These observations reveal a circular dichroism in the angle resolved emission with an asymmetry between forward and backward scattering (i.e., 0 degrees and 180 degrees to the light beam) which can exceed 12%. Since the initial state is an atomiclike spherically symmetric orbital, this strongly suggests that the asymmetry is caused by final-state effects dependent on the chiral geometry of the molecule. These findings are confirmed by electron multiple scattering calculations of the photoionization dynamics in the electric-dipole approximation.