All forms of waves can contain phase singularities1, 2, 3, 4. In the case of optical waves, a light beam with a phase singularity carries orbital angular momentum, and such beams have found a range of applications in optical manipulation, quantum information and astronomy3, 4, 5, 6, 7, 8, 9. Here we report the generation of an electron beam with a phase singularity propagating in free space, which we achieve by passing a plane electron wave through a spiral phase plate constructed naturally from a stack of graphite thin films. The interference pattern between the final beam and a plane electron wave in a transmission electron microscope shows the ‘Y’-like defect pattern characteristic of a beam carrying a phase singularity with a topological charge equal to one. This fundamentally new electron degree of freedom could find application in a number of research areas, as is the case for polarized electron beams.