This paper investigates the construction of social problems and the claims-making process to understand how racist populist discourse socially constructs racialised immigrants as a threat. Using a critical race discourse analysis of three speeches on immigration of the former US president Donald Trump, I investigate how he constructed and presented his claims in a manner to incite a social movement opposed to racialised immigration. This analysis does not uncover any new evidence about Trump and his position on race. Rather, I propose that in order to conduct a well-rounded analysis of racist populist speeches, we must engage in a contextualised analysis of social problems instead of focusing on the traditional constructionist analysis of social problems. I use Critical Race Theory as a theoretical framework to provide an understanding of how populist claims-makers draw on socially embedded racism as a vehicle to gain support from an audience which is often primed to receive the racist anti-immigration messages to construct racialised immigration as a social problem. Furthermore, I argue that we must look beyond the simple social construction of a claim to analyse the content of a claim and the context in which claims are made. I argue that rather than accepting all claims as credible, we can and should evaluate the validity of claims about social threats by considering the social conditions in which these claims are constructed.