Reducing fossil fuel supply is necessary to meet the Paris Agreement goal to keep warming “well below 2°C”. Yet, the Paris Agreement is silent on the topic of fossil fuels. This paper outlines reasons why it is important that Parties to the Agreement find ways to more explicitly address the phasing out of fossil fuel production under the UNFCCC. Describe how countries aiming to keep fossil fuel supply in line with Paris goals could articulate and report their actions within the current architecture of the Agreement. Also outline specific mechanisms of the Paris Agreement through which issues related to the curtailment of fossil fuel supply can be addressed. Mapping out a transition away from fossil fuels – and facilitating this transition under the auspices of the UNFCCC – can enhance the ambition and effectiveness of national and international climate mitigation efforts.