Abstract We demonstrate a method for calculating the neutral B -meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b -quarks. Our computation is performed on the “2+1” flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a ≈ 0 . 11 fm ( a − 1 = 1 . 729 GeV) and a lattice spatial volume of approximately (1 . 8 fm) $^{3}$. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy- light meson SU (2) chiral perturbation theory. For the b -quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the B -meson decay constant to O ( α$_{s}$pa ) using one-loop lattice perturbation theory. We present initial results for the SU (3)-breaking ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ = f$_{B}$$_{s}$ √ B$_{B}$$_{s}$/f$_{B}$$_{d}$ √ B$_{B}$$_{d}$ , thereby demonstrating the viability of the method. For the ratio of decay constants, we find f$_{B}$$_{s}$/f$_{B}$$_{d}$ = 1 . 15(12) and for the ratio of mixing matrix elements, we find ξ = 1 . 13(12), where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected O (1 /m$_{b}$ ) effects. PACS numbers: 12.38.Gc, 12.15.Hh, 14.40.Nd 2