The invention relates to method for operating an internal combustion engine that has at least two combustion chambers, of which at least one is operated at a substoichiometric air-fuel ratio and of which at least another is operated at a superstoichiometric air-fuel ratio. The outlet of the internal combustion engine is connected to an exhaust gas system in which a three-way catalytic converter is arranged in the flow direction of an exhaust gas through an exhaust gas channel, and an exhaust gas heat-recovery device is arranged downstream from the three-way catalytic converter. It is provided for the unburned fuel components of the combustion chamber that is operated at a substoichiometric air-fuel ratio to be exothermally reacted with the residual oxygen from the combustion chamber that is operated at a superstoichiometric air-fuel ratio on the three-way catalytic converter, whereby the exhaust gas temperature is raised so that the exhaust gas heat-recovery device can recover a portion of the exhaust gas enthalpy downstream from the three-way catalytic converter.