Lithospheric-scale transform faults play an important role in the dynamics of global plate motion. Near-surface deformation fields for such faults are relatively well documented by satellite geodesy, strain measurements and earthquake source studies, and deeper crustal structure has been imaged by seismic profiling. Relatively little is known, however, about deformation taking place in the subcrustal lithosphere--that is, the width and depth of the region associated with the deformation, the transition between deformed and undeformed lithosphere and the interaction between lithospheric and asthenospheric mantle flow at the plate boundary. Here we present evidence for a narrow, approximately 20-km-wide, subcrustal anisotropic zone of fault-parallel mineral alignment beneath the Dead Sea transform, obtained from an inversion of shear-wave splitting observations along a dense receiver profile. The geometry of this zone and the contrast between distinct anisotropic domains suggest subhorizontal mantle flow within a vertical boundary layer that extends through the entire lithosphere and accommodates the transform motion between the African and Arabian plates within this relatively narrow zone.