  We present a lattice determination of the $\Lambda$ parameter in three-flavor
QCD and the strong coupling at the Z pole mass. Computing the nonperturbative
running of the coupling in the range from $0.2\,$GeV to $70\,$GeV, and using
experimental input values for the masses and decay constants of the pion and
the kaon, we obtain $\Lambda_{\overline{\rm MS}}^{(3)}=341(12)\,$MeV. The
nonperturbative running up to very high energies guarantees that systematic
effects associated with perturbation theory are well under control. Using the
four-loop prediction for $\Lambda_{\overline{\rm
MS}}^{(5)}/\Lambda_{\overline{\rm MS}}^{(3)}$ yields
$\alpha^{(5)}_{\overline{\rm MS}}(m_{\rm Z}) = 0.11852(84)$.
