The TeV gamma-ray point source HESS J1832−093 remains unidentified despite extensive multiwavelength 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 XMMU J183245−0921539 and its relation to HESS J1832−093, we performed deeper follow-up observations in X-rays with Chandra and Swift to improve source localization and to investigate time variability. We observed an increase of the X-ray flux by a factor of ∼6 in the Chandra data compared to previous observations. The source is point-like for Chandra and its updated position is only 0.3 arcsec offset from 2MASS J18324516−0921545, confirming the association with this infrared source. Subsequent Swift target of opportunity observations resulted in a lower flux, again compatible with the one previously measured with XMM–Newton, indicating a variability time-scale 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. Furthermore, observations to characterize the optical counterpart as well as to search for orbital periodicity are needed to confirm this scenario.