We report a temperature-dependent scanning tunneling microscopy study of Na adsorption on the Si(111)-(7 X 7) surface by cooling the surface from room temperature to 80 K. While at room temperature Na atoms can diffuse freely on the surface to form a two-dimensional gas, their motion is confined within the 7 X 7 half-unit cells at 160 K. With further cooling to 80 K, Na atoms become localized within individual "basins." The estimated diffusion barriers of Na atoms on the Si(111)-(7 X 7) surface and nature of interaction among them agree well with our theoretical predictions.