A technique has been developed for producing transmission diffraction gratings suitable for use in the extreme ultraviolet. Thin self-supporting films of a transparent material are overlaid with several thousand opaque metallic strips per mm. Gratings with 2100, 2400, and 5675 1/mm have been produced and tested. Representative spectra over the wavelength range from 17.2 to 40.0 nm are given for a grating consisting of a 120 nm thick Al support layer overlaid with 2400, 34 nm thick, Ag strips/mm. The absolute transmittance is ~13% at 30 nm, and the efficiency in the first order is ~16%. The observed resolution of 0.2 nm is acceptable for many of the potential applications. These gratings have several advantages over the two presently available alternatives in the extreme ultraviolet (i.e., reflection gratings used at grazing incidence and free-standing metallic wire transmission gratings). Fabrication is relatively quick, simple, and cheap. The support layer can also serve as a filter and help conduct excessive heat away. Higher line densities and hence higher resolutions are possible, and when used at normal incidence the spectra are aberration free. Suitable materials, component thicknesses, and line densities can be chosen to produce a grating of optimum characteristics for a particular application.