Energy recovery linacs (ERLs) are an emerging generation of accelerators that promises to revolutionize the fields of high-energy physics and photon sciences. These accelerators combine the advantages of linear accelerators with that of storage rings, and augur the delivery of electron beams of unprecedented power and quality. The use of superconducting radio-frequency cavities converts ERLs into nearly perfect ''perpetuum mobile'' accelerators, wherein the beam is accelerated to the desired energy, used, and then yields the energy back to the rf field. However, one potential weakness of these devices is transverse beam breakup instability that could severely limit the available beam current. In this paper, I propose a novel method of suppressing these dangerous effects via a natural phenomenon in the accelerators, viz., the chromaticity of the transverse motion.