The partial oxidation of methane to methanol catalyzed by Cu-exchanged zeolites involves at present a three-step procedure that requires changing reaction conditions along the catalytic cycle. In this work we present an alternative catalytic cycle for selective methane conversion to methanol using as active species small Cu5 clusters supported on CHA zeolite. Periodic DFT calculations show that molecular O2 is easily activated on Cu5 clusters producing bi-coordinated O atoms able to dissociate homolytically a CH bond from CH4 and to react with the radical-like non-adsorbed methyl intermediate formed producing methanol, while competitive overoxidation to CO2 is energetically disfavored. The present mechanistic study opens a new avenue to design catalytic materials based on their ability to stabilize radical species.