  Bhabha scattering data recorded at \sqrt{s}=189 GeV by the L3 detector at LEP
are used to measure the running of the effective fine-structure constant for
spacelike momentum transfers. The results are alpha^-1(-2.1 GeV^2) -
alpha^-1(-6.25 GeV^2) = 0.78 +/- 0.26 alpha^-1(-12.25 GeV^2) - alpha^-1(-3434
GeV^2) = 3.80 +/- 1.29, in agreement with theoretical predictions.
