A first order phase transition is found in liquid carbon using atomistic simulation methods and Brenner{close_quote}s bond order potential. The phase line is terminated by a critical point at 8801thinspthinspK and 10.56thinspthinspGPa and by a triple point on the graphite melting line at 5133thinspthinspK and 1.88thinspthinspGPa. The phase change is associated with density and structural changes. The low-density liquid is predominantly sp bonded with little sp{sup 3} character. The high-density liquid is mostly sp{sup 3} bonded with little sp character. This is the first nonempirical evidence of a liquid-liquid transition between thermodynamically stable fluids. {copyright} {ital 1999} {ital The American Physical Society}