We present charged-particle guiding structures capable of confining energetic electron beams to micron-scale transverse dimensions on the surface of a chip. The guiding structures consist of a periodic arrangement of microfabricated electrostatic lenses. We formulate approximate analytical expressions for charged-particle trajectories through these guides, and we design an example guiding structure based on a mesa (stack) of alternating metal and dielectric layers. The example structure is amenable to modern microfabrication techniques, and we show, via particle-in-cell simulations, that electron beams with energies from 1 keV to 1 MeV and beam current densities> 1 kA/cm 2 should be stably confined with guides of this design. These guiding structures may enable enhanced interactions between electron beams and high-frequency electromagnetic waves for applications in THz-frequency vacuum electronics or light-driven accelerators.