The UA1 Collaboration has recently improved its measurement of the beauty production cross-section by including explicit measurements of b b correlations. Using these data we have determined the strong coupling constant α s . The comparison of the measured cross-section for 2-body final states with O ( α s 3 ) QCD predictions yields a measurement of α s (20 GeV) = 0.145 −0.010 exp −0.016 th +0.012 +0.013 , corresponding to α s ( M z ) = 0.113 −0.006 exp −0.009 th +0.007 +0.008 . This is the first theoretically well-defined measurement of α s from a purely hadronic production process. Evaluating α s from cross-sections at different Q 2 -values we find that the running of α s is needed for internal consistency of the UA1 data.