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Although individual radio pulses from pulsars vary in amplitude from pulse to pulse, their height distribution in general does not extend to amplitudes more than 10 times the mean. Two notable exceptions are the Crab pulsar and PSR B1937+21 (Lundgren 1995, Cognard et al. 1996 and references therein) which occasionally emit single radio pulses that have amplitudes more than 100 times the mean. Here we report on the detection of short time-scale, extremely large amplitude radio pulses from the nearby millisecond pulsar PSR J0437–4715. The events we have observed are distinguished by having peak flux densities in excess of 10 times the average pulse amplitude, and occur only within a very narrow (80 µs) window centered on the main pulse.