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Abstract Beyond our Solar System, aurorae have been inferred from radio observations of isolated brown dwarfs^1,2. Within our Solar System, giant planets have auroral emission with signatures across the electromagnetic spectrum including infrared emission of H₃⁺and methane. Isolated brown dwarfs with auroral signatures in the radio have been searched for corresponding infrared features, but only null detections have been reported³. CWISEP J193518.59-154620.3. (W1935 for short) is an isolated brown dwarf with a temperature of approximately 482 K. Here we report James Webb Space Telescope observations of strong methane emission from W1935 at 3.326 μm. Atmospheric modelling leads us to conclude that a temperature inversion of approximately 300 K centred at 1–10 mbar replicates the feature. This represents an atmospheric temperature inversion for a Jupiter-like atmosphere without irradiation from a host star. A plausible explanation for the strong inversion is heating by auroral processes, although other internal and external dynamical processes cannot be ruled out. The best-fitting model rules out the contribution of H₃⁺emission, which is prominent in Solar System gas giants. However, this is consistent with rapid destruction of H₃⁺at the higher pressure where the W1935 emission originates⁴.