One consequence of the special theory of relativity is that no signal can cause an effect outside the source light cone, the space-time surface on which light rays emanate from the source. Violation of this principle of relativistic causality leads to paradoxes, such as that of an effect preceding its cause. Recent experiments on optical pulse propagation in so-called 'fast-light' media--which are characterized by a wave group velocity upsilon(g) exceeding the vacuum speed of light c or taking on negative values--have led to renewed debate about the definition of the information velocity upsilon(i). One view is that upsilon(i) = upsilon(g) (ref. 4), which would violate causality, while another is that upsilon(i) = c in all situations, which would preserve causality. Here we find that the time to detect information propagating through a fast-light medium is slightly longer than the time required to detect the same information travelling through a vacuum, even though upsilon(g) in the medium vastly exceeds c. Our observations are therefore consistent with relativistic causality and help to resolve the controversies surrounding superluminal pulse propagation.