The performance characteristics of a solid-state electrochemical cell have been examined for the catalytic conversion of carbon dioxide and hydrogen to methane and oxygen. The electrolyte, made up of yttria-stabilized zirconia (YSZ), served the dual function of (a) a support material for the platinum catalyst, and (b) an oxygen ion-conducting membrane for the removal of surface oxygen formed during the reaction. The results indicate a linear increase in reaction rate with DC bias applied across the solid electrolyte. The reaction proceeds by way of a stepwise abstraction of oxygen atoms from carbon dioxide and hydrogenation of surface carbon to methane. The rate-limiting step is found to be the transport of oxygen ions through the solid electrolyte.