H1 and ZEUS have published single-differential cross sections for inclusive D∗±-meson production in deep-inelastic ep scattering at HERA from their respective final data sets. These cross sections are combined in the common visible phase-space region of photon virtuality Q2> 5 GeV2, electron inelasticity 0.02 < y < 0.7 and the D∗± meson’s transverse momentum pT(D∗) > 1.5 GeV and pseudorapidity |η(D∗)| < 1.5. The combination procedure takes into account all correlations, yielding significantly reduced experimental uncertainties. Double-differential cross sections d2σ/dQ2dy are combined with earlier D∗± data, extending the kinematic range down to Q2> 1.5 GeV2. Perturbative next-to-leading-order QCD predictions are compared to the results.