The liquid-liquid transition (LLT), in which a single-component liquid transforms into another one via a first-order phase transition, is an intriguing phenomenon that has changed our perception of the liquid state. LLTs have been predicted from computer simulations of water(1,2), silicon(3), carbon dioxide(4), carbon(5), hydrogen(6) and nitrogen(7). Experimental evidence has been found mostly in supercooled (that is, metastable) liquids such as Y2O3-Al2O3 mixtures(8), water(9) and other molecular liquids(10-12). However, the LLT in supercooled liquids often occurs simultaneously with crystallization, making it difficult to separate the two phenomena(13). A liquid-liquid critical point (LLCP), similar to the gas-liquid critical point, has been predicted at the end of the LLT line that separates the low- and high-density liquids in some cases, but has not yet been experimentally observed for any materials. This putative LLCP has been invoked to explain the thermodynamic anomalies of water(1). Here we report combined in situ density, X-ray diffraction and Raman scattering measurements that provide direct evidence for a first-order LLT and an LLCP in sulfur. The transformation manifests itself as a sharp density jump between the low- and high-density liquids and by distinct features in the pair distribution function. We observe a non-monotonic variation of the density jump with increasing temperature: it first increases and then decreases when moving away from the critical point. This behaviour is linked to the competing effects of density and entropy in driving the transition. The existence of a first-order LLT and a critical point in sulfur could provide insight into the anomalous behaviour of important liquids such as water.