Myanmar's much lauded but short-lived transition to a liberal capitalist order was marked by an upsurge in Islamophobia, anti-Muslim riots and the violent expulsion of hundreds of thousands of Rohingya into Bangladesh. Amid this conflagration, debates over ethnic inclusion, privilege and nationalism were prominent. Yet within these debates, even seemingly antagonistic positions incorporated the class-blindness characteristic of US liberal white privilege theory. In this article, we engage these debates by recalling an earlier radical theorisation of racial privilege that later liberal conceptions went on to displace. Taking capitalist class relations seriously, we argue that, for the poor Burman, ethnic privilege has been deeply ambiguous and ultimately harmful. Burman supremacy, in short, has served as ideological-material scaffolding for the enduring subjugation of the Burman proletariat itself. In order to elaborate our argument, we tell a critical history of Burman chauvinism in Myanmar - a history that reveals "Burman-ness" as a sign not simply of ethnic/racial privilege, but of class privilege as well.