  We estimate the QCD coupling constant from a lattice calculation of the
bottomonium spectrum. The second order perturbative expansion of the plaquette
expectation value is employed to determine alpha_S at a scale set by the 2S-1S
and 1P-1S level splittings. The latter are computed in NRQCD in a dynamical
gauge field background with two degenerate flavours of Wilson quarks at
intermediate masses and extrapolated to the chiral limit. Combining the N_f=2
result with the quenched result at equal lattice spacing we extrapolate to the
physical number of light flavours to find a value of alpha_{\bar MS}^{(5)}(m_Z)
= 0.1118(17). The error quoted covers both statistical and systematic
uncertainties in the scale determination. An additional 5% uncertainty comes
from the choice of the underlying sea quark formulation and from truncation
errors in perturbative expansions.
