  We demonstrate that recent measurements of Cosmic Microwave Background
temperature and polarization anisotropy made by the ACBAR, QUAD and BICEP
experiments substantially improve the cosmological constraints on possible
variations of the fine structure constant in the early universe. This data,
combined with the five year observations from the WMAP mission yield the
constraint alpha/alpha_0 = 0.987 \pm 0.012 at 68% c.l.. The inclusion of the
new HST constraints on the Hubble constant further increases the accuracy to
alpha/alpha_0 = 1.001 \pm 0.007 at 68% c.l., bringing possible deviations from
the current value below the 1% level and improving previous constraints by a
factor 3.
