We present near-infrared imaging of a sample of the faint, hard X-ray sources discovered in the 2001 Chandra Advanced CCD Imaging Spectrometer (ACIS)-I survey towards the Galactic Centre (GC) by Wang et al. These ∼800 discrete sources represent an important and previously undetected population within the Galaxy. From our Very Large Telescope observations of 77 X-ray sources, we identify candidate K-band counterparts to 75 per cent of the Chandra sources in our sample. The near-infrared magnitudes and colours of the majority of candidate counterparts are consistent with highly reddened stars, indicating that most of the Chandra sources are likely to be accreting binaries at or near the GC.