  In this Letter, we provide a determination of the coupling constant in
three-flavor quantum chromodynamics (QCD),
$\alpha^{\overline{\mathrm{MS}}}_s(\mu)$, for $\overline{\mathrm{MS}}$
renormalization scales $\mu \in (1,\,2)$ GeV. The computation uses gauge field
configuration ensembles with $\mathcal{O}(a)$-improved Wilson-clover fermions
generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach
is based on current-current correlation functions and has never been applied
before in this context. We convert the results perturbatively to the QCD
$\Lambda$-parameter and obtain $\Lambda_{\overline{\mathrm{MS}}}^{N_f=3} = 342
\pm 17$ MeV, which agrees with the world average published by the Particle Data
Group and has competing precision. The latter was made possible by a unique
combination of state-of-the-art CLS ensembles with very fine lattice spacings,
further reduction of discretization effects from a dedicated numerical
stochastic perturbation theory simulation, combining data from vector and
axial-vector channels and matching to high-order perturbation theory.
