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The muon capture reaction μ− + d → n + n + νμ in the doublet hyperfine state is studied using nuclear potentials and consistent currents derived in the chiral effective field theory, which are local and expressed in coordinate space (the so-called Norfolk models). Only the largest contribution due to the 1S0nn scattering state is considered. Particular attention is given to the estimate of theoretical uncertainty, for which four sources have been identified: 1) the model dependence, 2) the chiral-order convergence for the weak nuclear current, 3) the uncertainty in the single-nucleon axial form factor, and 4) the numerical technique adopted to solve the bound and scattering A = 2 systems. This last source of uncertainty has turned out to be essentially negligible. For the 1S0 doublet muon capture rate ΓD(S01), we obtain ΓD(S01)=255.8(0.6)(4.4)(2.9) s−1, where the three errors come from the first three sources of uncertainty. The value for ΓD(S01) obtained within this local chiral framework is compared with previous calculations and found in very good agreement.