We consider the asymmetric simple exclusion process (ASEP) with open boundary condition at the left boundary, where particles exit at rate γ and enter at rate α = γτ^2, and where τ is the asymmetry parameter in the bulk. At the right boundary, particles neither enter nor exit. By mapping the generator to the Hamiltonian of an XXZ quantum spin chain with reflection matrices, and using previously known results, we show algebraic symmetry and self-duality for the model.