The active sites and structure–activity relationship for methane activation over Cu-CHA were investigated by Density Functional Theory (DFT) calculations. [CuOCu]2+, [CuO2Cu]2+, [CuOH]+ and [CuO]+ were employed as possible active sites, but the Ab initio thermodynamics analysis results indicate that [CuO]+ is thermodynamically prohibitive. Methane activation in Cu-CHA proceeds through a homolytic mechanism, and the activity of Cu complexes in CH bond activation of methane follows the sequence [CuOH]+ (doublet) < [CuOCu]2+ (triplet) < [Cu2O2]2+ (triplet) in the six-member ring (6MR) and eight-member ring (8MR). In addition, the structure–activity relationship was established: The more reactive site is due to the ability to stabilize the methyl radical intermediate.