The $e^+e^- to pi^+ pi^- pi^0 chi_{bJ}$ ($J=0,~1,~2$) processes are studied using a 118~fb$^{-1}$ data sample collected at a center-of-mass energy of 10.867 GeV, in the $Upsilon(10860)$ energy range, with the Belle detector. The $pi^+ pi^- pi^0 chi_{b1}$, $pi^+pi^-pi^0chi_{b2}$, $omegachi_{b1}$ signals and the evidence of $omegachi_{b2}$ are observed for the first time and the cross sections are measured. No significant $pi^+pi^-pi^0chi_{b0}$ or $omegachi_{b0}$ signal is observed and 90% confidence level upper limits on the cross sections for these two processes are obtained. In the $pi^+pi^-pi^0$ invariant mass spectrum, significant non-$omega$ signals are also observed. We search for the $X(3872)$-like state with a hidden $bbar{b}$ component (named $X_b$) decaying into $omega Upsilon(1S)$; no significant signal is observed with a mass between $10.55$ and $10.65$ GeV/$c^2$.
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