The face is central to contemporary politics: it is photographed, pinned down, stored, documented, and presented as proof of identity in passports and ID cards. Automatic face recognition and face-processing systems are key to biopolitical control. However, Deleuze and Guattari argue that the face is a particular politics, and dismantling the face is also a politics. This paper explores what it might mean to dismantle the face, and what politics this might entail. It examines prosopagnosia, or face-blindness, as described by Oliver Sacks and exemplified by Chuck Close's paintings, which see the face as landscape. It asks whether the use of grid and screen in Close's portraits amounts to a dismantling of the face, and compares his approach to that seen in Francis Bacon's heads. It argues that Close's portraits trace a politics of becomings, a distribution of the sensible where we cannot, and do not, know who we are.