Self-modulation of an electron beam in a plasma has been observed. The propagation of a long (several plasma wavelengths) electron bunch in an overdense plasma resulted in the production of multiple bunches via the self-modulation instability. Using a combination of a radio-frequency deflector and a dipole spectrometer, the time and energy structure of the self-modulated beam was measured. The longitudinal phase space measurement showed the modulation of a long electron bunch into three bunches with an approximately 200  keV/c amplitude momentum modulation. Demonstrating this effect is a breakthrough for proton-driven plasma accelerator schemes aiming to utilize the same physical effect.