We demonstrate experimentally that the relativistic electron flow in a dense plasma can be efficiently confined and guided in targets exhibiting a high-resistivity-core-low-resistivity-cladding structure analogous to optical waveguides. The relativistic electron beam is shown to be confined to an area of the order of the core diameter (50 μm), which has the potential to substantially enhance the coupling efficiency of electrons to the compressed fusion fuel in the Fast Ignitor fusion in full-scale fusion experiments.