There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.