Lamellar eutectic structure in Al_0.7CoCrFeNi high-entropy alloy (HEA) is emerging as a promising candidate for structural applications because of its high strength-ductility combination. The alloy consists of a fine-scale lamellar fcc + B2 microstructure with high flow stresses > 1300 MPa under quasi-static tensile deformation and >10% ductility. The response to shear loading was not investigated so far. This is the first report on the shear deformation of a eutectic structured HEA and effect of precipitation on shear deformation. A split-Hopkinson pressure bar (SHPB) was used to compress the hat-shaped specimens to study the local dynamic shear response of the alloy. The change in the width of shear bands with respect to precipitation and deformation rates was studied. The precipitation of L1₂ phase did not delay the formation of adiabatic shear bands (ASB) or affect the ASB width significantly, however, the deformed region around ASB, consisting of high density of twins in fcc phase, was reduced from 80 µm to 20 µm in the stronger precipitation strengthened condition. We observe dynamic recrystallization of grains within ASBs and local mechanical response of individual eutectic lamellae before and after shear deformation and within the shear bands was examined using nano-indentation.