Browser fingerprinting aims to identify users or their devices, through scripts that execute in the users browser and collect information on software or hardware characteristics. It is used to track users or as an additional means of identification to improve security. Fingerprinting techniques have one significant limitation: they are unable to track individual users for an extended duration. This happens because browser fingerprints evolve over time, and these evolutions ultimately cause a fingerprint to be confused with those from other devices sharing similar hardware and software. In this paper, we report on a new technique that can significantly extend the tracking time of fingerprint-based tracking methods. Our technique, which we call DrawnApart, is a new GPU fingerprinting technique that identifies a device from the unique properties of its GPU stack. Specifically, we show that variations in speed among the multiple execution units that comprise a GPU can serve as a reliable and robust device signature, which can be collected using unprivileged JavaScript. We investigate the accuracy of DrawnApart under two scenarios. In the first scenario, our controlled experiments confirm that the technique is effective in distinguishing devices with similar hardware and software configurations, even when they are considered identical by current state-of-the-art fingerprinting algorithms. In the second scenario, we integrate a one-shot learning version of our technique into a state-of-the-art browser fingerprint tracking algorithm. We verify our technique through a large-scale experiment involving data collected from over 2,500 crowd-sourced devices over a period of several months and show it provides a boost of up to 67% to the median tracking duration, compared to the state-of-the-art method. DrawnApart makes two contributions to the state of the art in browser fingerprinting. On the conceptual front, it is the first work that explores the manufacturing differences between identical GPUs and the first to exploit these differences in a privacy context. On the practical front, it demonstrates a robust technique for distinguishing between machines with identical hardware and software configurations, a technique that delivers practical accuracy gains in a realistic setting.