We demonstrate that when a methanethiol adsorbed on the regular Cu͑111͒ surface, the dissociative structure is thermodynamically more stable than the intact one. The computational results show that at low temperature, the methanethiol adsorbate prefers the atop site of the regular Cu͑111͒ surface. As the temperature is increased, the S-H bond is broken and the methylthiolate favors the hollow sites. On the defected Cu͑111͒ surface, the dissociative configuration is still thermodynamically more stable than the nondissociative one. The calculation indicates that the hydrogen initially attached to the sulfur would like to form a bond with the copper surface rather than desorb from it. Even though both copper and gold are the noble metals, the stability of the methanethiol adsorption on the Cu͑111͒ substrate is almost the reverse of that on the Au͑111͒.