Solar geoengineering is gaining prominence in climate change debates as an issue worth studying; for some it is even a potential future policy option. We argue here against this increasing normalization of solar geoengineering as a speculative part of the climate policy portfolio. We contend, in particular, that solar geoengineering at planetary scale is not governable in a globally inclusive and just manner within the current international political system. We therefore call upon governments and the United Nations to take immediate and effective political control over the development of solar geoengineering technologies. Specifically, we advocate for an International Non-Use Agreement on Solar Geoengineering and outline the core elements of this proposal.