Scanning tunneling microscope images of the Si(111)2×1 surface are shown to reflect the spatial dependence of the bonding (π) and antibonding (π*) surface states. The surface states above and below the intrinsic gap are observed to have opposite parity, by the appearance of a 180° phase shift in the [011̄] corrugation with respect to tunneling into the π and π* states. A detailed voltage dependence of the phase of the surface charge density is obtained from spectroscopic images recorded simultaneously with the surface topograph.