Dispersive shock waves (DSWs) are expanding nonlinear wave trains that arise when dispersion regularizes a steepening front, a phenomenon observed in fluids, plasmas, optics, and superfluids. Here we report the first experimental observation of DSWs in an intense electron beam, using the University of Maryland Electron Ring (UMER). A localized induction-cell perturbation produced a negative density pulse that evolved into a leading soliton-like peak followed by an expanding train of oscillations. The leading peak satisfied soliton scaling laws for $(width{)}^2$ vs inverse amplitude and velocity vs amplitude, while the total wave-train width increased linearly with time, consistent with Korteweg-de Vries (KdV) predictions. Successive peaks showed decreasing amplitude and velocity toward the trailing edge, in agreement with dispersive shock ordering. These results demonstrate that intense charged particle beams provide a new laboratory platform for studying dispersive hydrodynamics, extending nonlinear wave physics into the high-intensity beam regime.