  We observe the build-up of a matter wave interference pattern from single
atom detection events in a double-slit experiment. The interference arises from
two overlapping atom laser beams extracted from a Rubidium Bose-Einstein
condensate. Our detector is a high-finesse optical cavity which realizes the
quantum measurement of the presence of an atom and thereby projects delocalized
atoms into a state with zero or one atom in the resonator. The experiment
reveals simultaneously the granular and the wave nature of matter.
