For the past half century, our understanding of how the interactions between electrons affect the low-temperature properties of metals has been based on the Landau theory of a Fermi liquid. In recent times, however, there have been an increasingly large number of examples in which the predictions of the Fermi-liquid theory appear to be violated. Although the qualitative reasons for the breakdown are generally understood, the specific quantum states that replace the Fermi liquid remain in many cases unclear. Here we describe an example of such a breakdown where the non-Fermi-liquid properties can be interpreted. We show that the thermal and electrical resistivities in high-purity samples of the d-electron metal ZrZn2 at low temperatures have T and T 5/3 temperature dependences, respectively: these are the signatures of the 'marginal' Fermi-liquid state, expected to arise from effective long-range spin-spin interactions in a metal on the border of metallic ferromagnetism in three dimensions. The marginal Fermi liquid provides a link between the conventional Fermi liquid and more exotic non-Fermi-liquid states that are of growing interest in condensed matter physics. The idea of a marginal Fermi liquid has also arisen in other contexts - for example, in the phenomenology of the normal state of the copper oxide superconductors, and in studies of relativistic plasmas and of nuclear matter.