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No spin-singlet $b \bar b$ quarkonium state has yet been observed. In thispaper we discuss the production of the singlet P-wave $b\bar{b}$ and $c\bar{c}$$^1P_1$ states $h_b$ and $h_c$. We consider two possibilities. In the first the$^1P_1$ states are produced via the electromagnetic cascades $\ups(3S) \to\eta_b(2S) + \gamma \to h_b + \gamma \gamma \to \eta_b +\gamma\gamma\gamma $and $\psi'\to \eta_c' + \gamma \to h_c + \gamma \gamma \to \eta_c +\gamma\gamma\gamma$. A more promising process consists of single piontransition to the $^1P_1$ state followed by the radiative transition to the$1^1S_0$ state: $\ups(3S)\to h_b + \pi^0 \to \eta_b + \pi^0 +\gamma$ and $\psi'\to h_c + \pi^0 \to \eta_c + \pi^0 +\gamma$. For a million $\ups(3S)$ or$\psi'$'s produced we expect these processes to produce several hundred events.Comment: 13 pages, LaTeX, 1 figure, to be published Phys. Rev. D. Some  equation numbers and one table number correcte

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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