  The incoming Imaging X-ray Polarimetry Explorer (IXPE) observations of X-ray
binaries provide a new tool to investigate the underlying accretion geometry.
Here we report the first measurements of X-ray polarization of the
extra-galactic black-hole X-ray binary LMC X$-$3. We find a polarization
fraction of $\sim 3%$ at a polarization angle of $\sim 135^\circ$ in the $2-8$
keV energy band with statistical significance at the 7$\sigma$ level. This
polarization measurement significantly exceeds the minimum detectable
polarization threshold of 1.2% for the source, ascertained at a 99% confidence
level within the $2-8$ keV energy band. The simultaneous spectro-polarimetric
fitting of NICER, Swift/XRT, and IXPE revealed the presence of a disc with a
temperature of $\sim$1 keV and a Comptonized component with a power-law index
of $\sim$ 2.4, confirming the soft nature of the source. The polarization
degree increases with energy from $\sim$3% in the $2-5.7$ keV band to $\sim$9%
in the $5.7-8$ keV band, while the polarization angle is energy independent.
The observed energy dependence and the sudden jump of polarization fraction
above 5 keV supports the idea of a static slab coronal geometry for the
Comptonizing medium of LMC X$-$3.
