We study Shubnikov-de Haas oscillations in single crystals of TaAs and find a previously undetected two-dimensional quantum oscillation that does not belong to the bulk Fermi surface. We cannot find an impurity phase consistent with our observations, and extensive diffraction measurements have not shown the presence of known impurity phases. We conjecture that the frequency originates from surface states that are sensitive to surface disorder. One candidate is the interference of coherent quasiparticles traversing two distinct Fermi arcs on the [001] crystallographic surface. The frequency and effective mass quantitatively agree with predictions of density functional theory and previous angle-resolved photoemission spectroscopy measurements of the Fermi arcs.