Extensive studies of metals and alloys have observed that nanotwins lead to strengthening, but the role of nanotwins in ceramics is not well established. We compare here the shear strength and the deformation mechanism of nanotwinned boron-rich boron carbide (B13C2) with the perfect crystal under both pure shear and biaxial shear deformations. We find that the intrinsic shear strength of crystalline B13C2 is higher than that of crystalline boron carbide (B4C). But nanotwins in B13C2 lower the strength, making it softer than crystalline B4C. This reduction in strength of nanotwinned B13C2 arises from the interaction of the twin boundary with the C-B-C chains that connect the B12 icosahedra.