Recent scientific advances have introduced the possibility of engineering the climate system to lower ambient temperatures without lowering greenhouse gas concentrations. This possibility has created an intense debate given the ethical, moral and scientific questions it raises. In this paper I examine the economic issues introduced when geoengineering becomes available in a standard two-period two-country model where strategic interaction leads to suboptimal mitigation. Geoengineering introduces the possibility of technical substitution away from mitigation, but it also affects the strategic interaction across countries: mitigation decisions made in the first period directly affect the geoengineering decisions made in the second period. With similar countries, I find the strategic effect creates greater incentives for free-riding on mitigation, but with asymmetric countries, the strategic effect that arises from the prospect of geoengineering can induce inefficiently high mitigation levels in equilibrium.