The number of migration museums is growing all over the world. These new museums seek to actively shape debates about immigration, and they often rely on immigrants’ personal stories to engage museum visitors and immigrant communities in dialogue. The article uses the case study of France’s National Museum of the History of Immigration in Paris and its collection of personal stories (The Gallery of Gifts) to explore this new form of story-activism and our concepts of hospitality. Drawing on Hélène du Mazaubrun’s, Jacques Derrida’s, Joan Stavo-Debauge’s and Paul Ricoeur’s ideas about gifting, hospitality, and recognition, I examine some challenging politico-ethical questions prompted by these immigrant story exhibitions.