In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), alpha((MS) over bar)(s)(mu), for (MS) over bar renormalization scales is mu is an element of (1, 2) GeV. The computation uses gauge field configuration ensembles with 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 agplied before in this context. We convert the results perturbatively to the QCD Lambda parameter and obtain Lambda(Nf=3)((MS) over bar) = 342 +/- 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.