We obtained far-UV spectra of the prototypical Seyfert 2 galaxy NGC 1068 with the Hopkins Ultraviolet Telescope during the flight of Astro-1 aboard the space shuttle Columbia in 1990 December. In two separate observations of NGC 1068 lasting 2356 and 2692 s we used circular apertures of 18" and 30" diameter, respectively. The spectra reveal strong emission lines of C III lambda-977, N III lambda-991, Ly-beta, O VI lambda-lambda-1032, 1038, and He II lambda-1085, all seen for the first time in a Seyfert 2 galaxy. Longward of Ly-alpha the spectrum is similar to previous observations obtained with the IUE. Broad-line components are visible for both Ly-alpha and C IV. The relative ratios of broad Ly-alpha, C IV, and H-beta are typical of those seen in Seyfert 1 galaxies and QSOs. A flat, blue continuum is observed down to the Lyman limit imposed by interstellar absorption in our own Galaxy. Excess continuum emission is present through the 30" aperture which can plausibly be attributed to young stars in the starburst ring. The moderately strong C III lambda-977 and N III lambda-991 emission is unusual for an AGN, and the line ratios below Ly-alpha are similar to those seen in HUT observations of the Cygnus Loop supernova remnant. The ratios of C III] lambda-1909 to lambda-977 and N III] lambda-1750 to lambda-991 imply temperatures exceeding 26,700 K and 24,000 K, respectively. Since these temperatures are much higher than those typically encountered in photoionized gas with abundant C+2 and N+2 populations, shock heating should be reconsidered as an additional source of emission lines in the nucleus of NGC 1068. Shocks could arise from the interaction of an X-ray-heated wind from the nucleus with the surrounding interstellar medium, or from radio jets striking interstellar clouds. Shocks from supernovae in starburst regions near the active nucleus are not a likely explanation.