The characterisation of fast phenomena at the microscopic scale is required for the understanding of catastrophic responses of materials to loads and shocks, the processing of materials by optical or mechanical means, the processes involved in many key technologies such as additive manufacturing and microfluidics, and the mixing of fuels in combustion. Such processes are usually stochastic in nature and occur within the opaque interior volumes of materials or samples, with complex dynamics that evolve in all three dimensions at speeds exceeding many meters per second. There is therefore a need for the ability to record three-dimensional X-ray movies of irreversible processes with resolutions of micrometers and frame rates of microseconds. Here we demonstrate a method to achieve this by recording a stereo phase-contrast image pair in a single exposure. The two images are combined computationally to reconstruct a 3D model of the object. The method is extendable to more than two simultaneous views. When combined with megahertz pulse trains of X-ray free-electron lasers (XFELs) it will be possible to create movies able to resolve 3D trajectories with velocities of kilometers per second.