With the Australian Square Kilometre Array Pathfinder (ASKAP) we monitored the black hole candidate X-ray binary MAXI J1535--571 over seven epochs from 21 September to 2 October 2017. Using ASKAP observations, we studied the HI absorption spectrum from gas clouds along the line-of-sight and thereby constrained the distance to the source. The maximum negative radial velocities measured from the HI absorption spectra for MAXI J1535--571 and an extragalactic source in the same field of view are $-69pm4$ km s$^{-1}$ and $-89pm4$ km s$^{-1}$, respectively. This rules out the far kinematic distance ($9.3^{+0.5}_{-0.6}$ kpc), giving a most likely distance of $4.1^{+0.6}_{-0.5}$ kpc, with a strong upper limit of the tangent point at $6.7^{+0.1}_{-0.2}$ kpc. At our preferred distance, the peak unabsorbed luminosity of MAXI J1535--571 was $>78$ per cent of the Eddington luminosity, and shows that the soft-to-hard spectral state transition occurred at the very low luminosity of 1.2 -- 3.4 $times$ 10$^{-5}$ times the Eddington luminosity. Finally, this study highlights the capabilities of new wide-field radio telescopes to probe Galactic transient outbursts, by allowing us to observe both a target source and a background comparison source in a single telescope pointing.
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