The interaction of atomic hydrogen with the Cu(111) surface was studied by a combined experimental-theoretical approach, using infrared reflection absorption spectroscopy, temperature programmed desorption, and density functional theory (DFT). Adsorption of atomic hydrogen at 160 K is characterized by an anti-absorption mode at 754 cm(-1) and a broadband absorption in the IRRA spectra, related to adsorption of hydrogen on three-fold hollow surface sites and sub-surface sites, and the appearance of a sharp vibrational band at 1151 cm(-1) at high coverage, which is also associated with hydrogen adsorption on the surface. Annealing the hydrogen covered surface up to 200 K results in the disappearance of this vibrational band. Thermal desorption is characterized by a single feature at ∼295 K, with the leading edge at ∼250 K. The disappearance of the sharp Cu-H vibrational band suggests that with increasing temperature the surface hydrogen migrates to sub-surface sites prior to desorption from the surface. The presence of sub-surface hydrogen after annealing to 200 K is further demonstrated by using CO as a surface probe. Changes in the Cu-H vibration intensity are observed when cooling the adsorbed hydrogen at 180 K to 110 K, implying the migration of hydrogen. DFT calculations show that the most stable position for hydrogen adsorption on Cu(111) is on hollow surface sites, but that hydrogen can be trapped in the second sub-surface layer.