Resonances are among the clearest quantum mechanical signatures of scattering processes. Previously, shape resonances and Feshbach resonances have been observed in inelastic and reactive collisions involving atoms or diatomic molecules. Structure in the integral cross section has been observed in a handful of elastic collisions involving polyatomic molecules. The present paper presents the observation of shape resonances in the reactive scattering of a polyatomic molecule, NH3. A merged-beam study of the gas phase He(S-3(1)) + NH3 Penning ionization reaction dynamics is described in the collision energy range 3.3 mu eV < E-coll < 10 meV. In this energy range, the reaction rate is governed by long-range attraction. Peaks in the integral cross section are observed at collision energies of 1.8 meV and 7.3 meV and are assigned to l = 15,16 and l = 20,21 partial wave resonances, respectively. The experimental results are well reproduced by theoretical calculations with the short-range reaction probability P-sr = 0.035. No clear signature of the orbiting resonances is visible in the branching ratio between NH3+ and NH2+ formation. (C) 2015 AIP Publishing LLC.