The investigation of the electronic properties of semiconductor surfaces using scanning tunneling spectroscopy (STS) is often hindered by nonequilibrium transport of the injected charge carriers. We propose a correction method for the resulting systematic errors in STS data, which is demonstrated for the well-known Si(111)-(7 x 7) surface. The surface has an odd number of electrons per surface unit cell and is metallic above 20 K. We observe an energy gap in the ground state of this surface by STS at 0.3 K. After the correction, the measured width of the gap is 70 +/- 15 meV, which is compatible with previous less precise estimates. No sharp peak of the density of states at the Fermi level is observed, in contrast to proposed models for the Si(111)-(7 x 7) surface.