Fomalhaut b is a directly imaged object in the debris disk of the star Fomalhaut . It has been hypothesized to be a planet , however there are issues with the observed colours of the object that do not fit planetary models . An alternative hypothesis is that the object is a neutron star in the near fore- or background of Fomalhaut ’ s disk . We test if Fomalhaut b could be a neutron star using X-ray observations with Chandra ’ s HRC-I instrument in the energy range of 0.08–10 keV . We do not detect X-ray emission from either Fomalhaut b or the star Fomalhaut itself . Our nondetection corresponds to an upper limit on the X-ray flux of Fomalhaut b of F _ { \mathrm { X } } < 1.3 \times 10 ^ { -14 } erg cm ^ { -2 } s ^ { -1 } in the energy range 0.08–10 keV . For the A-type central star Fomalhaut , we derive an X-ray upper limit of L _ { \mathrm { X } } < 2.0 \times 10 ^ { 25 } erg s ^ { -1 } in the energy range 0.08–10 keV . Fomalhaut b ’ s X-ray non-detection constrains the parameter space for a possible neutron star significantly , implying surface temperatures lower than 91 000 K and distances closer than 13.3 pc to the solar system . In addition we find that reflected starlight from the central star fits the available optical detections of Fomalhaut b ; a smaller planet with a large ring system might explain such a scenario .