An attractive direction in next-generation information processing is the development of systems employing particles or quasiparticles other than electrons--ideally with low dissipation--as information carriers. One such candidate is the magnon: the quasiparticle associated with the eigen-excitations of magnetic materials known as spin waves. The realization of single-chip all-magnon information systems demands the development of circuits in which magnon currents can be manipulated by magnons themselves. Using a magnonic crystal--an artificial magnetic material--to enhance nonlinear magnon-magnon interactions, we have succeeded in the realization of magnon-by-magnon control, and the development of a magnon transistor. We present a proof of concept three-terminal device fabricated from an electrically insulating magnetic material. We demonstrate that the density of magnons flowing from the transistor's source to its drain can be decreased three orders of magnitude by the injection of magnons into the transistor's gate.