Propagating a short, relativistically intense laser pulse in a plasma channel makes it possible to generate comb-like electron beams – sequences of synchronized, low phase-space volume bunches with controllable energy difference. The tail of the pulse, confined in the accelerator cavity (electron density “bubble”), transversely flaps, as the pulse head steadily self-guides. The resulting oscillations of the cavity size cause periodic injection of electrons from ambient plasma, creating an energy comb with the number of components, their energy, and energy separation dependent on the channel radius and pulse length. Accumulation of noise (continuously injected charge) can be prevented using a negatively chirped drive pulse with a bandwidth close to a one-half of the carrier wavelength. These comb-like beams can drive tunable, multi-color γ-ray sources.