The narrow-line Seyfert 1 Galaxy 1H 0707−495 went into a low state from 2010 December to 2011 February, discovered by a monitoring campaign using the X-Ray Telescope on the Swift satellite. We triggered a 100 ks XMM–Newton observation of the source in 2011 January, revealing the source to have dropped by a factor of 10 in the soft band, below 1 keV, and a factor of 2 at 5 keV, compared with a long observation in 2008. The sharp spectral drop in the source usually seen around 7 keV now extends to lower energies, below 6 keV in our frame. The 2011 spectrum is well fitted by a relativistically blurred reflection spectrum similar to that which fits the 2008 data, except that the emission is now concentrated solely to the central part of the accretion disc. The irradiating source must lie within 1 gravitational radius of the event horizon of the black hole, which spins rapidly. Alternative models are briefly considered, but none has any simple physical interpretation.