A search for the neutron-unbound nucleus 21 C was performed via the single proton removal reaction from a beam of 22 N at 68 MeV/u. Neutrons were detected with the Modular Neutron Array (MoNA) in coincidence with 20 C fragments. No evidence for a low-lying state was found, and the reconstructed 20 C+n decay energy spectrum could be described with an s-wave line shape with a scattering length limit of |a s | < 2.8 fm, consistent with shell model predictions. A comparison with a renormalized zero-range three-body model suggests that 22 C is bound by less than 70 keV.