This paper explores the communicative architecture of reception at the peak of Europe's 2015–2016 “migration crisis.” Drawing on fieldwork at one of Europe's outer borders—the Greek island of Chios—the paper examines the border as a site where refugee and migrant reception takes place and where the parameters of Europe's ethico‐political response to the “crisis” are set. The paper demonstrates that the continent's double requirement of security and care produces a new and highly ambivalent moral order, hospitability. Constituted through techno‐symbolic networks of mediation, hospitability reaffirms dominant theorizations of the border as an order of power and exclusion but goes beyond these in highlighting micro‐connections of solidarity that simultaneously coexist with and attempt to challenge this order.