A handful of enigmatic Jupiter-mass objects have been discovered orbiting millisecond pulsars.  Only one such object, PSR J2322-2650b, resembles a hot Jupiter due to its minimum density of 1.8 g/cm^3 and its ~1900 K temperature.  We used JWST to observe its emission spectrum across an entire orbit, finding--in stark contrast to every known exoplanet orbiting a main-sequence star--an atmosphere rich in molecular carbon (C3, C2) with strong westward winds.  Our observations open up a new exoplanetary chemical regime (ultra-high C/O ratio of >100 and C/N ratio of >10,000) and dynamical regime (ultra-fast rotation with external irradiation) to observational study. The extreme carbon enrichment poses a severe challenge to the current understanding of low-mass pulsar companions, which were expected to consist of a wider range of elements due to their origins as stripped stellar cores.