  We report on an X-ray polarimetric observation of the high-mass X-ray binary
LMC X-1 in the high/soft state, obtained by the Imaging X-ray Polarimetry
Explorer (IXPE) in October 2022. The measured polarization is below the minimum
detectable polarization of 1.1 per cent (at the 99 per cent confidence level).
Simultaneously, the source was observed with the NICER, NuSTAR and SRG/ART-XC
instruments, which enabled spectral decomposition into a dominant thermal
component and a Comptonized one. The low 2-8 keV polarization of the source did
not allow for strong constraints on the black-hole spin and inclination of the
accretion disc. However, if the orbital inclination of about 36 degrees is
assumed, then the upper limit is consistent with predictions for pure thermal
emission from geometrically thin and optically thick discs. Assuming the
polarization degree of the Comptonization component to be 0, 4, or 10 per cent,
and oriented perpendicular to the polarization of the disc emission (in turn
assumed to be perpendicular to the large scale ionization cone orientation
detected in the optical band), an upper limit to the polarization of the disc
emission of 1.0, 0.9 or 0.9 per cent, respectively, is found (at the 99 per
cent confidence level).
