We report the observation of electronic coherence between core-level vacancies created at different atomic sites in a molecule. This coherence, which is a fundamental aspect of quantum mechanics, can be probed by measuring the interference of the x-ray fluorescence emitted from the two sites. We demonstrate this technique by measuring the coherence between the carbon K-shell vacancies in carbon dioxide (CO2) molecules. Our results show that the coherence is preserved for a time scale that is long compared to the lifetime of the core-level vacancies. This opens up the possibility of using core-level coherence to study the dynamics of molecules and other complex systems.