The two outer triangular caustics (regions of infinite magnification) of a close binary microlens move much faster than the components of the binary themselves, and can even exceed the speed of light. When ϵ > 1, where ϵ c is the caustic speed, the usual formalism for calculating the lens magnification breaks down. We develop a new formalism that makes use of the gravitational analog of the Liénard-Wiechert potential. We find that as the binary speeds up, the caustics undergo several related

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... nges: First, their position in space drifts. Second, they rotate about their own axes so that they no longer have a cusp facing the binary center of mass. Third, they grow larger and dramatically so for ϵ >> 1. Fourth, they grow weaker roughly in proportion to their increasing size. Superluminal caustic-crossing events are probably not uncommon, but they are difficult to observe.