Abell 1201 is a massive galaxy cluster at z=0.169 with a brightest cluster galaxy ( BCG ) that acts as a gravitational lens to a background source at z=0.451 . The lensing configuration is unusual , with a single bright arc formed at small radius ( \sim 2 arcsec ) , where stars and dark matter are both expected to contribute substantially to the total lensing mass . Here , we present deep spectroscopic observations of the Abell 1201 BCG with MUSE , which reveal emission lines from a faint counter-image , opposite to the main arc , at a radius of 0.6 arcsec . We explore models in which the lensing mass is described by a combination of stellar mass and a standard dark-matter halo . The counter-image is not predicted in such models , unless the dark-matter component is negligible , which would imply an extremely heavy stellar initial mass function ( IMF ) in this galaxy . We consider two modifications to the model which can produce the observed configuration without resorting to extreme IMFs . Imposing a radial gradient in the stellar mass-to-light ratio , \Upsilon , can generate a counter-image close to the observed position if \Upsilon increases by \ga 60 per cent within the inner \sim 1 arcsec ( e.g . variation from a Milky-Way-like to a Salpeter-like IMF ) . Alternatively , the counter-image can be produced by introducing a central super-massive black hole . The required mass is M _ { BH } = ( 1.3 \pm 0.6 ) \times 10 ^ { 10 } M _ { \odot } , which is comparable to the largest black holes known to date , several of which are also hosted by BCGs . We comment on future observations which promise to distinguish between these alternatives .