Amid a crisis of political representation, Chile ran an institutional experiment. After a month of riots, lootings and human rights violations, in November 2019, the Chilean Parliament proposed the creation of a fully elected convention with the one objective of writing a new Constitution. The 155 members were elected in October 2020 and 62% of them were non-professional politicians but environmental activists, members of indigenous communities or feminist leaders. Inspired by the ideas of representative claim proposed by Saward and performativity coined by Butler, we analysed their inauguration speeches to observe how they attempted to constitute themselves as political representatives. We found that they relied upon four types of speech appeal in their political claims-making. We refer to these as the Agonistic (whereby the claim-maker purported to speak for “us” as opposed to “them”); the Climactic (whereby the claim-maker offered themselves as an embodiment of a historical coming of age for a particular group); the Biographical (the claim-maker focuses upon their personal qualities of identity with empathy towards a group); and the Trustee (whereby, adhering to more conventional rhetoric of representation, a claim-maker sets out their qualification to acknowledge and look after the interests and values of a particular group).