Proposals for the intentional engineering of the Earth's climate through techniques of solar radiation management (SRM) have been accompanied by profound questions of governance. As the purpose, goals and motivations of SRM are considerations of paramount importance, governance must not only encompass risks and unintended consequences, but also intent. In this chapter, I pose two questions as these relate to SRM and governance. Firstly, should we be entertaining the thought of research or deployment of SRM and its governance, i.e. is SRM a legitimate object of governance, and if so under what conditions? And, linked to this, secondly, is SRM governable, particularly within democratic political systems? Arguing that SRM is a political artefact I will describe some potential problems it may present for democratic governance. I will go on to sketch a brief history of governance discussions and initiatives concerning SRM. In doing so I will observe that the boundary work of learned societies, some academics and others has attempted to legitimise SRM research as an object of governance, defining governance contours and thresholds, underpinned by normative principles. I will review some recent personal experiences of the first attempt to move from words to actions, in terms of governing a SRM research project within a framework for responsible innovation. I will finally review the results of emerging public and stakeholder dialogue exercises which reveal that while attitudes towards SRM research are nuanced and ambivalent, publics and many stakeholders have great antipathy, even hostility, towards SRM deployment. As research is projected through to deployment both become simultaneously framed and the legitimacy of SRM research questioned. Conditions for acceptable deployment that include the need for international agreement and governance may be perceived as being highly implausible, with concerns that SRM may prove incompatible with governance based on democratic principles, and may generate unprecedented forms of geopolitical conflict. Given these considerations I will conclude that the question of whether SRM, and its research, is a legitimate object of governance remains to be democratically decided, if indeed it ever can be.