Einstein's theory of special relativity and the principle of causality(1-4) imply that the speed of any moving object cannot exceed that of light in a vacuum (c). Nevertheless, there exist various proposals(5-18) for observing faster-than-c propagation of light pulses, using anomalous dispersion near an absorption line(4,6-8), nonlinear(9) and linear gain lines(10-18), or tunnelling barriers(19). However, in all previous experimental demonstrations, the light pulses experienced either very large absorption(7) or severe reshaping(9,19), resulting in controversies over the interpretation. Here we use gain-assisted linear anomalous dispersion to demonstrate superluminal light propagation in atomic caesium gas. The group velocity of a laser pulse in this region exceeds c and can even become negative(16,17), while the shape of the pulse is preserved. We measure a group-velocity index of n(g) = -310(+/-5); in practice, this means that a light pulse propagating through the atomic vapour cell appears at the exit side so much earlier than if it had propagated the same distance in a vacuum that the peak of the pulse appears to leave the cell before entering it. The observed superluminal light pulse propagation is not at odds with causality, being a direct consequence of classical interference between its different frequency components in an anomalous dispersion region.