Accurate motion capture of aerial robots in 3D is a key enabler for autonomous operation in indoor environments such as warehouses or factories, as well as driving forward research in these areas. The most commonly used solutions at present are optical motion capture (e.g. VICON) and Ultrawideband (UWB), but these are costly and cumbersome to deploy, due to their requirement of multiple cameras/anchors spaced around the tracking area. They also require the drone to be modified to carry an active or passive marker. In this work, we present an inexpensive system that can be rapidly installed, based on single-chip millimeter wave (mmWave) radar. Importantly, the drone does not need to be modified or equipped with any markers, as we exploit the Doppler signals from the rotating propellers. Furthermore, 3D tracking is possible from a single point, greatly simplifying deployment. We develop a novel deep neural network and demonstrate decimeter level 3D tracking at 10Hz, achieving better performance than classical baselines. Our hope is that this low-cost system will act to catalyse inexpensive drone research and increased autonomy.