We report the discovery of a Neptune-size planet (Rp = 3.0 Re) in the Hyades Cluster. The host star is in a binary system, comprising a K5V star and M7/8V star with a projected separation of 40 AU. The planet orbits the primary star with an orbital period of 17.3 days and a transit duration of 3 hours. The host star is bright (V=11.2, J=9.1) and so may be a good target for precise radial velocity measurements. K2-136A c is the first Neptune-sized planet to be found orbiting in a binary system within an open cluster. The Hyades is the nearest star cluster to the Sun, has an age of 625-750 Myr, and forms one of the fundamental rungs in the distance ladder; understanding the planet population in such a well-studied cluster can help us understand and set constraints on the formation and evolution of planetary systems.