The halo structure of 31Ne is studied using 1n-removal reactions on C and Pb targets at 230 MeV/nucleon. A combined analysis of the cross sections of these nuclear and Coulomb dominated reactions that feed directly the 30Ne ground-state reveals 31Ne to have a small neutron separation energy, 0.15(-0.10)(+0.16) MeV, and spin-parity 3/2-. Consistency of the data with reaction and large-scale shell-model calculations identifies 31Ne as deformed and having a significant p-wave halo component, suggesting that halos are more frequent occurrences at the neutron drip line.