A prism spectrum of PSR B0540-69, the 50 ms pulsar in the Large Magellanic Cloud, was obtained with the Faint Object Spectrograph on the Hubble Space Telescope. This is only the second pulsar spectrum that has been observed in the optical. The 2500-5500 Å spectrum shows a smooth continuum with several broad emission lines. The lines are emitted by the extended nebula surrounding B0540-69. Less than 30% of the total flux in the spectrum can be contributed by the synchrotron nebula surrounding the pulsar; the time-averaged emission from the pulsar must be the dominant source of the continuum. The observed spectral index, α, of the continuum, where flux density Sν = Kνα μJy, is -2.5 +/- 0.2 between 2500 and 4500 Å. Using E(B - V) = 0.20 +/- 0.05 gives a de-extincted spectral index α0 = -1.6 +/- 0.4. This intrinsic spectral index is significantly different from that of the Crab pulsar in the optical α0 = 0.11 +/- 0.13. Unless E(B - V) ~ 0.5, the intrinsic spectral index of time-averaged pulsar radiation must vary as much from pulsar to pulsar in the high-frequency regime as it does in the radio.Based in part on observations with the Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.