Objective. At the balanced intersection of human and machine adaptation is found the optimally functioning brain-computer interface (BCI). In this study, we report a novel experiment of BCI controlling a robotic quadcopter in three-dimensional (3D) physical space using noninvasive scalp electroencephalogram (EEG) in human subjects. We then quantify the performance of this system using metrics suitable for asynchronous BCI. Lastly, we examine the impact that the operation of a real world device has on subjects' control in comparison to a 2D virtual cursor task. Approach. Five human subjects were trained to modulate their sensorimotor rhythms to control an AR Drone navigating a 3D physical space. Visual feedback was provided via a forward facing camera on the hull of the drone. Main results. Individual subjects were able to accurately acquire up to 90.5% of all valid targets presented while travelling at an average straight-line speed of 0.69 m s-1. Significance. Freely exploring and interacting with the world around us is a crucial element of autonomy that is lost in the context of neurodegenerative disease. Brain-computer interfaces are systems that aim to restore or enhance a user's ability to interact with the environment via a computer and through the use of only thought. We demonstrate for the first time the ability to control a flying robot in 3D physical space using noninvasive scalp recorded EEG in humans. Our work indicates the potential of noninvasive EEG-based BCI systems for accomplish complex control in 3D physical space. The present study may serve as a framework for the investigation of multidimensional noninvasive BCI control in a physical environment using telepresence robotics.