Dissociative chemisorption of methane on Ni(100) and Ni(111) surfaces with preadsorbed potassium in the coverage range 0-0.12 monolayer (ML) has been measured at 475 and 500 K. The results show that the methane sticking probability is strongly diminished by the presence of potassium. An explanation for this surprising inhibition has been sought by performing large-scale density functional theory calculations of the dissociative chemisorption of methane on Ni(100) and Ni(111) surfaces with and without preadsorbed potassium. The calculations show that the barrier for dissociation of methane is increased by about 0.2 eV when 0.125 ML potassium is preadsorbed on both nickel surfaces. In the transition state of the dissociating methane molecule a dipole moment is induced. It is shown that the increase of the barrier is largely given by the interaction between the induced dipole moment in the transition state and the electrostatic field induced by the potassium adatoms.