  We report the discovery of the first giant pulses from an extragalactic radio
pulsar. Observations of PSR B0540-69 in the Large Magellanic Cloud made with
the Parkes radio telescope at 1.38 GHz show single pulses with energy more than
5000 times that of the average pulse energy. This is only the second young
pulsar, after the Crab, to show giant pulse emission. Similar to the Crab
pulsar, the giant pulses occur in two distinct phase ranges and have
significant arrival time jitter within these ranges. The location of the giant
pulses appears to lag the peak of the (sinusoidal) X-ray profile by 0.37 and
0.64 phase, although absolute timing between the radio and X-ray data is not
yet secure. The dispersion measure of the giant pulses is 146.5 pc/cc, in
agreement with the detection of the pulsar at 0.64 GHz by Manchester et al.
(1993). The giant pulses are scatter broadened at 1.4 GHz with an exponential
scattering time of 0.4 ms and have an emission bandwidth of at least 256 MHz.
In 8 hr of integration we have failed to detect any integrated flux density
from the pulsar to a level of 13 microJy, assuming a duty cycle of 10%. This
implies the spectral index between 0.64 and 1.38 GHz is steeper than -4.4.
