Isolated diatomic molecules of iodine monochloride (ICL) were photodissociated by a beam of Linearly polarized light, and the resulting ground-state CL atom photofragments were detected by a method that is sensitive to the handedness (helicity) of the electronic angular momentum. It was found that this helicity oscillates between "topspin" and "backspin" as a function of the wavelength of the dissociating light. The helicity originates solely from the (de Broglie) matter-wave interference of multiple dissociating pathways of the electronic excited states of ICI. These measurements can be related to the identity and to the detailed shapes of the dissociating pathways, thus demonstrating that it is possible to probe repulsive states by spectroscopic means.