This paper presents Neutron Capture Enhanced Particle Therapy (NCEPT), a method for enhancing the radiation dose delivered to a tumour relative to surrounding healthy tissues during proton and carbon ion therapy by capturing thermal neutrons produced inside the treatment volume during irradiation. NCEPT utilises extant and in-development boron-10 and gadolinium-157-based drugs from the related field of neutron capture therapy. Using Monte Carlo simulations, we demonstrate that a typical proton or carbon ion therapy treatment plan generates an approximately uniform thermal neutron field within the target volume, centred around the beam path. The tissue concentrations of neutron capture agents required to obtain an arbitrary 10% increase in biological effective dose are estimated for realistic treatment plans, and compared to concentrations previously reported in the literature. We conclude that the proposed method is theoretically feasible, and can provide a worthwhile improvement in the dose delivered to the tumour relative to healthy tissue with readily achievable concentrations of neutron capture enhancement drugs.