  We report a study of the hadronic transitions
$\chi_{bJ}(2P)\to\omega\Upsilon(1S)$, with $\omega\to\pi^{+}\pi^{-}\pi^{0}$,
using $28.2\times10^6~\Upsilon(3S)$ mesons recorded by the Belle detector. We
present the first evidence for the near--threshold transition
$\chi_{b0}(2P)\to\omega\Upsilon(1S)$, the analog of the charm sector decay
$\chi_{c1}(3872)\to\omega J/\psi$, with a branching fraction of
$B\big(\chi_{b0}(2P)\to\omega\Upsilon(1S)\big) =
\big(0.55\pm0.19\pm0.07\big)\%$. We also obtain branching fractions of
$B\big(\chi_{b1}(2P)\to\omega\Upsilon(1S)\big) =
\big(2.39{}^{+0.20}_{-0.19}\pm0.24\big)\%$ and
$B\big(\chi_{b2}(2P)\to\omega\Upsilon(1S)\big) =
\big(0.47{}^{+0.13}_{-0.12}\pm0.06\big)\%$, confirming the measurement of the
$\omega$ transitions of the $J=1,2~P$--wave states. The ratio for the $J=2$ to
$J=1$ transitions is also measured and found to differ by 3.3 standard
deviations from the expected value in the QCD multipole expansion.
