The Neanderthals were a Eurasian human species of the genus Homo that disappeared approximately 30,000 years ago. The cause or causes of their extinction continues to intrigue specialists and non-specialists alike. Here a contributory role for Transmissible Spongiform Encephalopathies (TSEs) is suggested. TSEs could have infected Neanderthal groups as a result of general cannibalistic activity and brain tissue consumption in particular. Further infection could then have taken place through continued cannibalistic activity or via shared used of infected stone tools. A modern human hunter-gatherer proxy has been developed and applied as a hypothetical model to the Neanderthals. This hypothesis suggests that the impact of TSEs on the Neanderthals could have been dramatic and have played a large part in contributing to the processes of Neanderthal extinction.