We report observations of the atmospheric transmission spectrum of the sub-Neptune exoplanet GJ 3470 b taken using the Near-Infrared Camera on JWST. Combined with two archival Hubble Space Telescope/Wide-Field Camera 3 transit observations and 15 archival Spitzer transit observations, we detect water, methane, sulfur dioxide, and carbon dioxide in the atmosphere of GJ 3470 b, each with a significance of >3σ. GJ 3470 b is the lowest-mass—and coldest—exoplanet known to show a substantial sulfur dioxide feature in its spectrum, at M p = 11.2 M ⊕ and T eq = 600 K. This indicates that disequilibrium photochemistry drives sulfur dioxide production in exoplanet atmospheres over a wider range of masses and temperatures than has been reported or expected. The water, carbon dioxide, and sulfur dioxide abundances we measure indicate an atmospheric metallicity of approximately 100× solar. We see further evidence for disequilibrium chemistry in our inferred methane abundance, which is significantly lower than expected from equilibrium models consistent with our measured water and carbon dioxide abundances.