  We have searched for exclusive production of exotic charmonia in the reaction
$\mu^+~N \rightarrow \mu^+ (J\!/\!\psi\pi^+\pi^-)\pi^{\pm}~N'$ using COMPASS
data collected with incoming muons of 160 GeV/$c$ and 200 GeV/$c$ momentum. In
the $J\!/\!\psi\pi^+\pi^-$ mass distribution we observe a signal with a
statistical significance of 4.1 $\sigma$. Its mass and width are consistent
with those of the $X(3872)$. The shape of the $\pi^+\pi^-$ mass distribution
from the observed decay into $J\!/\!\psi\pi^+\pi^-$ shows disagreement with
previous observations for $X(3872)$. The observed signal may be interpreted as
a possible evidence of a new charmonium state. It could be associated with a
neutral partner of $X(3872)$ with $C = -1$ predicted by a tetraquark model. The
product of cross section and branching fraction of the decay of the observed
state into $J\!/\!\psi\pi^+\pi^-$ is determined to be
71$\pm$28(stat)$\pm$39(syst) pb.
