A novel technique for β-delayed neutron spectroscopy has been demonstrated using trapped ions. The neutron-energy spectrum is reconstructed by measuring the time of flight of the nuclear recoil following neutron emission, thereby avoiding all the challenges associated with neutron detection, such as backgrounds from scattered neutrons and γ rays and complicated detector-response functions. (137)I(+) ions delivered from a (252)Cf source were confined in a linear Paul trap surrounded by radiation detectors, and the β-delayed neutron-energy spectrum and branching ratio were determined by detecting the β(-) and recoil ions in coincidence. Systematic effects were explored by determining the branching ratio three ways. Improvements to achieve higher detection efficiency, better energy resolution, and a lower neutron-energy threshold are proposed.