Transmission spectroscopy has enabled unprecedented insights into the makeup of exoplanet atmospheres. A transmission spectrum combines contributions from a planet's morning and evening limbs, but these limbs may have different temperatures, compositions, and aerosol properties due to atmospheric circulation. High-resolution ground-based observations have detected limb asymmetry on several ultra-hot (>2000 K) exoplanets, but space-based investigation into limb asymmetry is in its infancy, and limb asymmetry's prevalence in the broader exoplanet population remains unexplored. We find evidence for limb asymmetry on the exoplanet WASP-107b via transmission spectroscopy from 2.5 to 4.0 micrometers with JWST/NIRCam. This is one of the first low-resolution space-based measurements of limb asymmetry and is unique because, at 770 K, WASP-107b is in a relatively cool regime where planetary terminators are expected to be homogeneous. These observations imply a difference in temperature and cloud properties between WASP-107b's limbs, challenging our models of limb asymmetry in this cooler regime.