A storage ring measurement of the rate coefficient for the production of neutral Ar in e + ArH+ collisions is described. It is found that the recombination rate is too small to measure at low centre-of-mass energies but the combined rate coefficient for dissociative recombination and dissociative excitation increases above 2.5 eV displaying peaks centred at 7.5 eV, 16 and 26 eV. Calculated potential energy curves for the ground and excited states of ArH+ are presented and these aid in the elucidation of the recombination and excitation processes observed at higher energies. The implications for plasma modelling are discussed.