Most materials expand upon heating. Although rare, some materials expand on cooling, and are said to exhibit negative thermal expansion (NTE); but the property is exhibited in only one crystallographic direction. Such materials include silicon and germanium at very low temperature (<100 K) and, at room temperature, glasses in the titania-silica family, Kevlar, carbon fibres, anisotropic Invar Fe-Ni alloys, ZrW2O3 (ref. 4) and certain molecular networks. NTE materials can be combined with materials demonstrating a positive thermal expansion coefficient to fabricate composites exhibiting an overall zero thermal expansion (ZTE). ZTE materials are useful because they do not undergo thermal shock on rapid heating or cooling. The need for such composites could be avoided if ZTE materials were available in a pure form. Here we show that an electrically conductive intermetallic compound, YbGaGe, can exhibit nearly ZTE--that is, negligible volume change between 100 and 400 K. We suggest that this response is due to a temperature-induced valence transition in the Yb atoms. ZTE materials are desirable to prevent or reduce resulting strain or internal stresses in systems subject to large temperature fluctuations, such as in space applications and thermomechanical actuators.