In this Letter we report a spectroscopic confirmation of the association of ( catalog HLX-1 ) , the brightest ultra-luminous X-ray source , with the galaxy ESOÂ 243-49 . At the host galaxy distance of 95 Mpc , the maximum observed 0.2 – 10 keV luminosity is 1.2 \times 10 ^ { 42 } erg s ^ { -1 } . This luminosity is \sim 400 times above the Eddington limit for a 20 M _ { \odot } black hole , and has been interpreted as implying an accreting intermediate mass black hole with a mass in excess of 500 M _ { \odot } ( assuming the luminosity is a factor of 10 above the Eddington value ) . However , a number of other ultra-luminous X-ray sources have been later identified as background active galaxies or foreground sources . It has recently been claimed that ( catalog HLX-1 ) could be a quiescent neutron star X-ray binary at a Galactic distance of only 2.5 kpc , so a definitive association with the host galaxy is crucial in order to confirm the nature of the object . Here we report the detection of the H \alpha emission line for the recently identified optical counterpart at a redshift consistent with that of ESO 243-49 . This finding definitively places ( catalog HLX-1 ) inside ESO 243-49 , confirming the extreme maximum luminosity and strengthening the case for it containing an accreting intermediate mass black hole of more than 500 M _ { \odot } .