The rare decay B → πl þ l − arises from b → d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B → π tensor form factor f T . Together with the vector and scalar form factors f þ and f 0 from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B → π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BRðB þ → π þ μ þ μ − Þ ¼ 20.4ð2.1Þ × 10 −9 in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) Motivation.-Hadron decays that proceed through flavor-changing neutral currents may be sensitive to new physics, because their leading standard model contributions are loop suppressed. Here we study the semileptonic decay B → πl þ l − , which proceeds through a b → d transition. Hadronic effects in this decay are parametrized by three form factors. In this Letter, we present the first ab initio QCD calculation of the tensor form factor f T , based on lattice-QCD work that also yielded the vector and scalar form factors, f þ and f 0 [1]. Lattice QCD has several advantages over other approaches to the form factors [2][3][4][5][6][7][8][9], particularly in providing a path to controlled uncertainties that can be systematically reduced [10].The LHCb experiment recently made the first observation of B þ → π þ μ þ μ − [11], while the B factories have set limits on the e þ e − and τ þ τ − channels [12][13][14]. Below we