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Analyzing $\Upsilon(nS)$ decays acquired with the CLEO detector operating at the CESR $e^+e^-$ collider, we measure for the first time the product branching fractions ${\cal B}[\Upsilon(nS)\to\gamma\chi_{b}((n-1)P_J)] \times {\cal B}[\chi_{b}(n-1)P_J)\to X_i]$ for $n=2$ and 3, where $X_i$ denotes, for each $i$, one of the fourteen exclusive light-hadron final states for which we observe significant signals in both $\chi_b(1P_J)$ and $\chi_b(2P_J)$ decays.
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