  Using data taken with the CLEO II detector at the Cornell Electron Storage
Ring, we have determined the ratio of branching fractions: $R_{\gamma} \equiv
\Gamma(\Upsilon(1S) \rightarrow \gamma gg)/\Gamma(\Upsilon(1S) \rightarrow ggg)
= (2.75 \pm 0.04(stat.) \pm 0.15(syst.))%$. From this ratio, we have determined
the QCD scale parameter $\Lambda_{\overline{MS}}$ (defined in the modified
minimal subtraction scheme) to be $\Lambda_{\overline{MS}}= 233 \pm 11 \pm 59$
MeV, from which we determine a value for the strong coupling constant
$\alpha_{s}(M_{\Upsilon(1S)}) = 0.163 \pm 0.002 \pm 0.014$, or
$\alpha_{s}(M_{Z}) = 0.110 \pm 0.001 \pm 0.007$.
