Backdoors pose a serious threat to machine learning, as they can compromise the integrity of security-critical systems, such as self-driving cars. While different defenses have been proposed to address this threat, they all rely on the assumption that the hardware on which the learning models are executed during inference is trusted. In this paper, we challenge this assumption and introduce a backdoor attack that completely resides within a common hardware accelerator for machine learning. Outside of the accelerator, neither the learning model nor the software is manipulated, so that current defenses fail. To make this attack practical, we overcome two challenges: First, as memory on a hardware accelerator is severely limited, we introduce the concept of a minimal backdoor that deviates as little as possible from the original model and is activated by replacing a few model parameters only. Second, we develop a configurable hardware trojan that can be provisioned with the backdoor and performs a replacement only when the specific target model is processed. We demonstrate the practical feasibility of our attack by implanting our hardware trojan into the Xilinx Vitis AI DPU, a commercial machine-learning accelerator. We configure the trojan with a minimal backdoor for a traffic-sign recognition system. The backdoor replaces only 30 (0.069%) model parameters, yet it reliably manipulates the recognition once the input contains a backdoor trigger. Our attack expands the hardware circuit of the accelerator by 0.24% and induces no run-time overhead, rendering a detection hardly possible. Given the complex and highly distributed manufacturing process of current hardware, our work points to a new threat in machine learning that is inaccessible to current security mechanisms and calls for hardware to be manufactured only in fully trusted environments.