This paper outlines the IoT Databox model as a means of making the Internet of Things (IoT) accountable to individuals. Accountability is a key to building consumer trust and is mandated by the European Union's general data protection regulation (GDPR). We focus here on the 'external' data subject accountability requirement specified by GDPR and how meeting this requirement turns on surfacing the invisible actions and interactions of connected devices and the social arrangements in which they are embedded. The IoT Databox model is proposed as an in principle means of enabling accountability and providing individuals with the mechanisms needed to build trust into the IoT.