Neutron stimulated emission computed tomography (NSECT) is presented as a new technique for in vivo tomographic spectroscopic imaging. A full implementation of NSECT is intended to provide an elemental spectrum of the body or part of the body being interrogated at each voxel of a three-dimensional computed tomographic image. An external neutron beam illuminates the sample and some of these neutrons scatter inelastically, producing characteristic gamma emission from the scattering nuclei. These characteristic gamma rays are acquired by a gamma spectrometer and the emitting nucleus is identified by the emitted gamma energy. The neutron beam is scanned over the body in a geometry that allows for tomographic reconstruction. Tomographic images of each element in the spectrum can be reconstructed to represent the spatial distribution of elements within the sample. Here we offer proof of concept for the NSECT method, present the first single projection spectra acquired from multi-element phantoms, and discuss potential biomedical applications.