THE nature of gamma-ray bursters-astrophysical sources that emit abrupt bursts of gamma-rays-presents a long-standing question in high-energy astronomy. Soft gamma-ray repeaters (SGRs) are distinguished from classical gamma-ray bursters by the short duration, softer gamma-ray spectrum and recurrent activity of their outbursts(1-6). Millisecond-scale structure in these bursts suggests that SGRs are compact, and many models invoke neutron stars as the emitting objects(1,5). This idea is supported by the association of two SGRs, SGR0526-66 (ref. 6) and SGR1806-20 (ref. 7), with supernova remnants, SNR N49 and the radio nebula G10.0-0.3 respectively. Very recently, Kulkarni et al.(8,9) have suggested that a compact radio source in G10.0-0.3 corresponds to a young pulsar at the centre of this nebula, and can be identified with SGR1806-20. Here we report the detection of a burst from SGR1806-20 with the X-ray satellite ASCA(10), which allows us to identify the burster with a new X-ray source which we designate AX1805.7-2025. The burst is coincident in time with that detected by the BATSE(11,12) instrument on board the Compton Gamma Ray Observatory. This result provides strong evidence that SGRs are indeed neutron stars.