Counter-geoengineering is the idea that a country might seek or threaten to counteract the cooling effect of solar geoengineering through technical means. Although this concept has been mentioned with increasing frequency in commentary on geoengineering, it has received little scholarly attention. We offer a preliminary analysis. We begin by distinguishing two kinds of counter-geoengineering: countervailing with a warming agent, and neutralising with a physical disruption. Based on this distinction, we review prior suggestions and describe novel methods by which either method might be accomplished, within the constraints imposed by deep technical uncertainties and substantial technical challenges. We then reflect on the strategic requirements and motivations for developing counter geoengineering and use a simple game-theoretic framework to demonstrate how counter-geoengineering might interact with the free-driver dynamic of solar geoengineering to shape climate geopolitics. We find that any state that could credibly threaten counter-geoengineering would effectively have a veto over the use of solar geoengineering, which could reduce the prospects of unilateral deployment. Alternatively, the development of geoengineering and countergeoengineering capabilities could lead to dangerous brinkmanship. We conclude that the development of counter-geoengineering would face considerable practical obstacles and would signal continuing political failure to manage climate risks on a cooperative basis.