We present a search for the decay X(3872)→π+π−π0 in the
(772±11)×106Υ(4S)→BBˉ data sample collected at the
Belle detector, where the X(3872) is produced in B±→K±X(3872)
and B0→KS0X(3872) decays. We do not observe a signal, and set 90\%
credible upper limits for two different models of the decay processes: if the
decay products are distributed uniformly in phase space, B(X(3872)→π+π−π0)<1.3%; if M(π+π−) is concentrated near the mass
of the D0Dˉ0 pair in the process X(3872)→D0Dˉ∗0+c.c.→D0Dˉ0π0→π+π−π0, B(X(3872)→π+π−π0)<1.2×10−3