We have identified a satellite of the Trojan asteroid (3548) Eurybates in images obtained with the Hubble Space Telescope. The satellite has been detected on four separate epochs, 12 and 14 September 2018, 03 January 2020 and 19 July 2020. The satellite was not detected in observations on 11 and 21 December 2019 and 03 August 2020 when it was presumed to be within 0.4 arcsec of Eurybates where it is too faint to be detected against the scattered light from the primary. The satellite has a brightness consistent with an effective diameter of d2 = 1.2±0.4 km for a body with the same albedo as Eurybates. The projected separation from Eurybates ranged from s ~ 1700–2300 km and varied in position. The detections and non-detections are consistent with a range of possible orbits. Eurybates is one of the targets of the Lucy Discovery mission and the early detection of this satellite provides an opportunity for a significant expansion of the scientific return from this encounter.