The enigmatic downchirped signals, called "perytons," that are detected by radio telescopes in the GHz frequency range may be produced by an atmospheric phenomenon known as ball lightning (BL). If BLs act as nonstationary radio frequency cavities, their characteristic emission frequencies and evolution timescales are consistent with peryton observations, and so are general patterns in which BLs are known to occur. Based on this evidence, testable predictions are made that can confirm or rule out a causal connection between perytons and BLs. In either case, how perytons are searched for in observational data may warrant reconsideration because existing procedures may be discarding events that have the same nature as known perytons.