We analyzed data of the first 20-ks Chandra observations of the bright Fermi pulsar J0633+0632 and found a strong evidence of an absorption feature in its spectrum near 0.8 keV. This makes it the first γ-ray pulsar where an X-ray absorption feature is observed. Besides that, it is likely the coldest neutron star at the neutrino cooling stage. Finally, it powers an extended pulsar wind nebula whose shape suggests a high pulsar proper motion. Looking backwards the direction of the presumed proper motion we found a likely birthplace of the pulsar – the Rosette nebula, a 50-Myr active star-forming region located at the edge of a large molecular cloud.

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