The uncertainty principle, applied naively to the test masses of a laser interferometer gravitational wave detector, produces a standard quantum limit (SQL) on the interferometer's sensitivity. It has long been thought that beating this SQL would require a radical redesign of interferometers. We show that no redesign is needed at all. LIGO-II interferometers, as currently planned, can beat the SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their thermal noise can be pushed low enough. This is due to quantum correlations between photon shot noise and radiation pressure noise, produced by the LIGO-II signal-recycling mirror.