The electronic properties of the Be(0001) surface are investigated on the atomic scale at low temperature. Utilizing laterally resolved scanning tunneling spectroscopy (STS) a pronounced surface state is identified, additionally manifested by the observation of bias-dependent standing-wave patterns. Fourier analysis reveals a parabolic dispersive behavior, being characteristic for a two-dimensional free-electron gas confined to the Be(0001) surface. Moreover, signatures of the opening of inelastic phonon-mediated tunnel channels for electrons near the Fermi level are observed by STS.