Using data taken with the CLEO III detector at the Cornell Electron Storage Ring, we have investigated the direct photon spectrum in the decays Υ(1S) → γgg, Υ(2S) → γgg, Υ(3S) → γgg. The latter two of these are first measurements. Our analysis procedures differ from previous ones in the following ways: a) background estimates (primarily from π 0 decays) are based on isospin symmetry rather than a determination of the π 0 spectrum, which permits measurement of the Υ(2S) and Υ(3S) direct photon spectra without explicit corrections for π 0 backgrounds from, e.g., χ bJ states, b) we estimate the branching fractions with a parametrized functional form (exponential) used for the background, c) we use the high-statistics sample of Υ(2S)→ ππΥ(1S) to obtain a tagged-sample of Υ(1S)→ γ + X events, for which there are no QED backgrounds. We determine values for the ratio of the inclusive direct photon decay rate to that of the dominant three-gluon decay Υ → ggg (R γ = B(ggγ)/B(ggg)) to be: R γ (1S)=(2.70±0.01±0.13±0.24)%, R γ (2S)=(3.18±0.04±0.22±0.41)%, and R γ (3S)=(2.72±0.06±0.32±0.37)%, where the errors shown are statistical, systematic, and theoretical model-dependent, respectively. Given a value of Q 2 , one can estimate a value for the strong coupling constant α s (Q 2 ) from R γ .