The occurrence of lightning in a planetary atmosphere enables chemical processes to take place that would not occur under standard temperatures and pressures. Although much evidence has been reported for lightning on Venus, some searches have been negative and the existence of lightning has remained controversial. A definitive detection would be the confirmation of electromagnetic, whistler-mode waves propagating from the atmosphere to the ionosphere. Here we report observations of Venus' ionosphere that reveal strong, circularly polarized, electromagnetic waves with frequencies near 100Hz. The waves appear as bursts of radiation lasting 0.25 to 0.5s, and have the expected properties of whistler-mode signals generated by lightning discharges in Venus' clouds.