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Asteroid pairs, two objects that are not gravitationally bound to one another, but share a common origin, have been discovered in the Main belt and Hungaria populations. Such pairs are of major interest, as the study of their evolution under a variety of dynamical influences can indicate the time since the pair was created. To date, no asteroid pairs have been found in the Jovian Trojans, despite the presence of several binaries and collisional families in the population. The search for pairs in the Jovian Trojan population is of particular interest, given the importance of the Trojans as tracers of planetary migration during the Solar system's youth. Here we report a discovery of the first pair, (258656) 2002~ES$_{76}$ and 2013~CC$_{41}$, in the Jovian Trojans. The two objects are approximately the same size and are located very close to the L4 Lagrange point. Using numerical integrations, we find that the pair is at least $360$~Myr old, though its age could be as high as several Gyrs. The existence of the (258656) 2002~ES$_{76}$--2013~CC$_{41}$ pair implies there could be many such pairs scattered through the Trojan population. Our preferred formation mechanism for the newly discovered pair is through the dissociation of an ancient binary system, triggered by a sub-catastrophic impact, but we can not rule out rotation fission of a single object driven by YORP torques. A by-product of our work is an up-to-date catalog of Jovian Trojan proper elements, which we have made available for further studies.