The binary nature of the Galactic Centre X-ray source CXOGC J174536.1-285638

X-ray and near-IR surveys of the central 2x0.8 degrees of the Galactic Centre have revealed a population of X-ray bright massive stars. However, the nature of the emission, originating in a wind collision zone or via accretion onto a compact object, is uncertain. In order to address this we investigated the nature of the luminous X-ray source CXOGC J174536.1-285638. An analysis of the near-IR spectrum with a non-LTE model atmosphere code demonstrated that it was an highly luminous WN9h star, for which comparison to evolutionary tracks suggests an age of 2-2.5Myr and an initial mass of ~110Msun. The X-ray properties of CXOGC J174536.1-285638 resemble those of 3 of the WN9h stars within the Arches cluster and in turn other very massive WNLh colliding wind binaries. Simple analytical arguments demonstrate consistency between the X-ray emission and a putative WN9h+mid O V-III binary. However, we may not exclude a high mass X-ray binary interpretation, which, if correct, would provide a unique insight into the (post-SN) evolution of extremely massive stars. Irrespective of the nature of the secondary, CXOGC J174536.1-285638 adds to the growing list of known and candidate WNLh binaries. Of the subset of WNLh stars subject to a radial velocity survey, we find a lower limit to the binary fraction of ~45%; of interest for studies of massive stellar formation, given that they currently possess the highest dynamically determined masses of any type of star. [ABRIDGED]