Recent results indicate that the compact lenticular galaxy NGC 1277 in the Perseus Cluster contains a black hole of approximately 10 billion solar masses. This far exceeds the expected mass of the central black hole in a galaxy of the modest dimensions of NGC 1277. We suggest that this giant black hole was ejected from the nearby giant galaxy NGC 1275 and subsequently captured by NGC 1277. The ejection was the result of gravitational radiation recoil when two large black holes merged following the merger of two giant ellipticals that helped to form NGC 1275. The black hole wandered in the cluster core until it was captured in a close encounter with NGC 1277. The migration of black holes in clusters may be a common occurrence.