The design of a high-resolution photoelectron microscope (photoelectron emission microscope) is described. It is an oil-free ultrahigh-vacuum instrument utilizing electrostatic electron optics. New designs are presented for a specimen translator, cathode stage, aperture stop control, electrostatic hexapole stigmator, beam shutter, and camera system. These components could also be used in a low-energy electron microscope (LEEM). The theoretical resolution of this instrument is 5 nm for UV illumination near the photoemission threshold. The photoelectron microscope is now in operation at the University of Oregon, and it is achieving results within a factor of two of this design limit.