  We measure the neutral absorption towards the black hole X-ray binary system
LMC X-1 from six archival soft X-ray spectra obtained with the gratings and/or
CCD detectors on Chandra, XMM-Newton, and Swift. Four spectral models for the
soft continuum have been investigated. While the powerlaw model may
overestimate NH considerably, the others give consistent results. Taking the
lower metalicity of the Large Magellanic Cloud into account, we find equivalent
hydrogen column densities of N_H = (1.0-1.3)*10^22 cm^-2, with a systematic
dependence on the orbital phase. This variation of the neutral absorption can
nearly explain the orbital modulation of the soft X-ray flux recently detected
with the All Sky Monitor (ASM) on the Rossi X-ray Timing Explorer (RXTE).
