The cosmic radio spectrum is expected to show a strong absorption signal around redshift 20 that corresponds to the rise of the first stars; specifically, the stellar radiation turns on 21-cm absorption by atomic hydrogen. The EDGES global 21-cm experiment has detected the first such signal, finding a stronger absorption than the maximum expected. This absorption can be explained by invoking excess cooling of the cosmic gas induced by an interaction with dark matter. This would have far reaching consequences, including an upper limit on the mass of dark matter particles that conflicts with the expectations for WIMPs. Specific particle physics models are highly constrained, but observations will decide. In particular, we predict that 21-cm fluctuations at cosmic dawn are likely to be much larger than previously expected, exhibiting a specific signature that will be a clear test of the effect of dark matter.