Odd slip at solid-liquid interfaces, characterized by a velocity component perpendicular to the applied shear stress, introduces a novel class of odd transport phenomena with transverse momentum transfer at boundaries, distinct from odd viscosity, odd elasticity, or odd diffusivity. This effect arises on chiral active surfaces with persistent energy input and defined handedness, such as carpets of rotating biological or synthetic cilia with flexible anchoring. Although odd slip itself is dissipationless, its maintenance in active systems comes at an energetic cost, which we estimate from the microscopic model. With respect to its orientation dependence, odd slip can be classified as pseudo-scalar or pseudo-vectorial. We use a perturbative expansion to determine the resistance tensors of problems with different levels of broken symmetries. They reveal how the surface chirality and body asymmetry together violate the Onsager symmetry, but uphold the Onsager-Casimir reciprocity. Strikingly, suspensions of particles with odd slip embedded in a conventional Newtonian bulk fluid exhibit odd viscosity, providing a new minimal mechanism for its emergence beyond current microscopic models.