The Kuiper belt is a collection of small bodies (Kuiper belt objects, KBOs) that lie beyond the orbit of Neptune and which are believed to have formed contemporaneously with the planets. Their small size and great distance make them difficult to study. KBO 55636 (2002 TX300) is a member of the water-ice-rich Haumea KBO collisional family. The Haumea family are among the most highly reflective objects in the Solar System. Dynamical calculations indicate that the collision that created KBO 55636 occurred at least 1Gyr ago. Here we report observations of a multi-chord stellar occultation by KBO 55636, which occurred on 9 October 2009 UT. We find that it has a mean radius of 143+/-5km (assuming a circular solution). Allowing for possible elliptical shapes, we find a geometric albedo of in the V photometric band, which establishes that KBO 55636 is smaller than previously thought and that, like its parent body, it is highly reflective. The dynamical age implies either that KBO 55636 has an active resurfacing mechanism, or that fresh water-ice in the outer Solar System can persist for gigayear timescales.