The TeV gamma-ray point source HESSJ1832-093 remains unidentified despite extensive multi-wavelength studies. The gamma-ray emission could originate in a very compact pulsar wind nebula or an X-ray binary system composed of the X-ray source XMMU J183245-0921539 and a companion star (2MASS J18324516-0921545). To unveil the nature of XMMUJ183245-0921539 and its relation to HESSJ1832-093, we performed deeper follow-up observations in X-rays with Chandra and Swift to improve source localisation and to investigate time variability. We observed an increase of the X-ray flux by a factor ~6 in the Chandra data compared to previous observations. The source is point-like for Chandra and its updated position is only 0.3 offset from 2MASS J18324516-0921545, confirming the association with this infrared source. Subsequent Swift ToO observations resulted in a lower flux, again compatible with the one previously measured with XMM-Newton, indicating a variability timescale of the order of two months or shorter. The now established association of XMMU J183245-0921539 and 2MASS J18324516-0921545 and the observed variability in X-rays are strong evidence for binary nature of HESS J1832-093. Further observations to characterise the optical counterpart as well as to search for orbital periodicity are needed to confirm this scenario.