Search for $\Upsilon$(1S) $\to \gamma\eta$ and $\gamma\eta'$

Using a data sample of around 20,000,000 $\Upsilon$(1S) decays collected by the CLEO III detector at CESR, we present the results of a search for the exclusive decays $\Upsilon$(1S) into $\gamma \eta$ and $\Upsilon$(1S) into $\gamma \eta'$.