Large-amplitude electron density oscillations were observed on a Be(0001) surface by means of variable-temperature scanning tunneling microscopy. Fourier transforms of the images showed a ring of radius 2k(F), where k(F) is the Fermi wave vector of the Be(0001) surface state, This wavelength was expected from Friedel oscillations caused by electronic screening of surface defects, but the amplitude of the waves for energies near the Fermi energy was anomalously large and inconsistent with the Friedel concept of screening. The enhanced amplitude of the waves must be a many-body effect, either in the electron gas (possibly an incipient charge density wave) or in the response of the lattice (electron-phonon coupling).