Investigations of the thickness dependent electronic structure of ultrathin aluminium films deposited on Si(111) 7×7 using angle resolved photoelectron spectroscopy show the first experimental observation of quantum-well states in this system. Deposition at 100 K favours an abrupt and homogeneous interface and the growth of an epitaxial, quasi two-dimensional Al(111) overlayer of good crystalline quality, making possible the observation of overlayer states for thicknesses up to 30 Al monolayers. We obtain the decay length of the Al(111) surface state as well as the energy-dependent phase shift of the electron waves at the Al/Si interface.