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 cm ^ { -3 } pc , 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 \mu Jy , assuming a duty cycle of 10 % . This implies the spectral index between 0.64 and 1.38 GHz is steeper than –4.4 .