  The abundances of major carbon and oxygen bearing gases in the atmospheres of
giant exoplanets provide insights into atmospheric chemistry and planet
formation processes. Thermochemistry suggests that methane should be the
dominant carbon-bearing species below $\sim$1000 K over a range of plausible
atmospheric compositions; this is the case for the Solar System planets and has
been confirmed in the atmospheres of brown dwarfs and self-luminous directly
imaged exoplanets. However, methane has not yet been definitively detected with
space-based spectroscopy in the atmosphere of a transiting exoplanet, but a few
detections have been made with ground-based, high-resolution transit
spectroscopy including a tentative detection for WASP-80b. Here we report
transmission and emission spectra spanning 2.4-4.0 micrometers of the 825 K
warm Jupiter WASP-80b taken with JWST's NIRCam instrument, both of which show
strong evidence for methane at greater than 6-sigma significance. The derived
methane abundances from both viewing geometries are consistent with each other
and with solar to sub-solar C/O and ~5$\times$ solar metallicity, which is
consistent with theoretical predictions.
