High-resolution electron energy loss spectroscopy was used to investigate the low-energy collective excitations of the Cu (111) surface. Measurements showed a collective mode with an energy of 1.1 eV. The measured dispersion of the plasmon mode was negative. We suggest that this mode arises from the oscillation of electrons confined to the Cu (111) surface within quasi-two-dimensional Shockley surface states. Moreover, we show that the acousticlike mode theoretically proposed for the (111) surface of noble metals is not observed in copper. The behavior of the plasmon dispersion curve and the lack of the acoustic mode call for specific theoretical interpretations of the present experimental results.