  We present the first measurement of the surface magnetic field of a late-M
dwarf, LSR J1835+3259, with the help of the full-Stokes spectropolarimetry in
the bands of diatomic molecules. Our magnetic field measurements at different
rotational phases of the dwarf yielded one 5$\sigma$ and two 3$\sigma$
detections. The observational data have been obtained with the LRISp
polarimeter at the Keck observatory on August 22nd and 23rd, 2012. These data
have been compared against synthetic full-Stokes spectra in the bands of the
molecules CrH, FeH and TiO, which have been calculated for a range of the
stellar parameters and magnetic field strengths. Making use of
$\chi^2$-minimization and maximum likelihood estimation, we determine the net
magnetic field strength $B$ (and not flux $Bf$) of LSR J1835+3259 to $\sim5$
kG, mainly with the help of the Paschen-Back effect in the CrH lines. Our
measurements at different rotational phases suggest that the dwarf's surface
might be covered with strong small-scale magnetic fields. In addition, recent
findings of the hydrogen emission and the Stokes V signal in the Na I
near-infrared doublet indicate that the dwarf's surface magnetic field might be
changing rapidly giving rise to flare activity, similar to young dMe dwarfs. We
substantiate the substellar origin of LSR J1835+3259 by making use of our own
data as well as the photometric data from the all-sky surveys 2MASS and WISE.
