Observations with the Newton X-ray Multimirror Mission (XMM) show a strong periodic modulation at 6.67+/-0.03 hours of the X-ray source at the centre of the 2,000-year-old supernova remnant RCW 103. No fast pulsations are visible. If genetically tied to the supernova remnant, the source could either be an X-ray binary, comprising a compact object and a low-mass star in an eccentric orbit, or an isolated neutron star. In the latter case, its age-period combination would point to a peculiar magnetar, dramatically slowed-down, possibly by a supernova debris disc. Both scenarios require non-standard assumptions on the formation and evolution of compact objects in supernova explosions.