We report results from a study of hadronic transitions of the $chi_{bJ}(nP)$ states of bottomonium at Belle. The $P$-wave states are reconstructed in transitions to the $Upsilon(1S)$ with the emission of an $omega$ meson. The transitions of the $n=2$ triplet states provide a unique laboratory in which to study nonrelativistic quantum chromodynamics, as the kinematic threshold for production of an $omega$ and $Upsilon(1S)$ lies between the $J=0$ and $J=1$ states. A search for the $chi_{bJ}(3P)$ states is also reported.