Microbunching of a relativistic electron beam into a helix is examined analytically and in simulation. Helical microbunching is shown to occur naturally when an e beam interacts resonantly at the harmonics of the combined field of a helical magnetic undulator and an axisymmetric input laser beam. This type of interaction is proposed as a method to generate a strongly prebunched e beam for coherent emission of light with orbital angular momentum at virtually any wavelength. The results from the linear microbunching theory show excellent agreement with three-dimensional numerical simulations.