The femtosecond dissociation of HCl after core excitation has been studied through the resonant Auger decay. The spectra contain contributions from decay occurring at both "molecular" and "atomic" internuclear distances. We have observed a new interference mechanism in these spectra: An atomic spectral line develops into a negative spectral contribution, a "hole," when detuning the excitation energy from the maximum of the Cl2p(-1)sigma(*) resonance. Resonant x-ray scattering theory quantitatively explains this behavior as due to a novel destructive continuum-continuum interference between molecular and atomic contributions to the Auger decay.