  Context. The Metis coronagraph is one of the remote-sensing instruments of
the ESA/NASA Solar Orbiter mission. Metis is aimed at the study of the solar
atmosphere and solar wind by simultaneously acquiring images of the solar
corona at two different wavelengths; visible-light (VL) within a band ranging
from 580 nm to 640 nm, and in the HI Ly-alpha 121.6 +/- 10 nm ultraviolet (UV)
light. The visible-light channel includes a polarimeter with electro-optically
modulating Liquid Crystal Variable Retarders (LCVRs) to measure the linearly
polarized brightness of the K-corona to derive the electron density.
  Aims. In this paper, we present the first in-flight validation results of the
Metis polarimetric channel together with a comparison to the on-ground
calibrations. It is the validation of the first use in deep space (with hard
radiation environment) of an electro-optical device: a liquid crystal-based
polarimeter.
  Methods. We used the orientation of the K-corona's linear polarization vector
during the spacecraft roll maneuvers for the in-flight calibration.
  Results. The first in-flight validation of the Metis coronagraph on-board
Solar Orbiter shows a good agreement with the on-ground measurements. It
confirms the expected visible-light channel polarimetric performance. A final
comparison between the first pB obtained by Metis with the polarized brightness
(pB) obtained by the space-based coronagraph LASCO and the ground-based
coronagraph KCor shows the consistency of the Metis calibrated results.
