  The isospin-breaking decay $X(3872)\to(D^*\bar D+ \bar D^*D) \to\pi^0D\bar
D\to\pi^0\pi^+\pi^-$ is discussed. In its amplitude there is a triangle
logarithmic singularity, due to which the dominant contribution to
$BR(X(3872)\to\pi^0\pi^+\pi^-)$ comes from the production of the $\pi^+\pi^-$
system in a narrow interval of the invariant mass $m_{\pi^+\pi^-}$ near the
value of $2m_{D^0} \approx 3.73$ GeV. The analysis shows that
$BR(X(3872)\to\pi^0 \pi^+\pi^-)$ can be expected at the level of
$10^{-3}$--$10^{-4}$. This estimate includes, in particular, the assumption
that the $S$-wave inelastic scattering length $|\alpha''_{D^0\bar D^0
\to\pi^+\pi^-}|\approx1/(2m_{D^{*+}})\approx0.25\ \mbox{GeV}^{-1}$.
