Using data taken with the CLEO II detector at the Cornell Electron Sto
rage Ring, we have determined the ratio of branching fractions: R-gamm
a=Gamma(Upsilon(1S)--> gamma ilon(1S)-->ggg)=[2.75+/-0.04(stat)+/-0.15
(syst)]%. From this ratio, we have determined the QCD scale parameter
Lambda(<(MS)over bar>) (defined in the modified minimal subtraction sc
heme) to be Lambda(<(MS)over bar>)=233+/-11+/-59 MeV, from which we de
termine a value for the strong coupling constant alpha(s)(M-gamma(1S))
=0.163+/-0.002+/-0.014, or alpha(s)(M-Z)=0.110+/-0.001+/-0.007.