A neutron spectrometer is a device that measures the spectrum of the kinetic energy of neutrons. There are numerous applications that can profitably use a compact neutron spectrometer. For instance, fast neutron resonance radiography requires sufficiently high resolution (several percent) to identify the absorption spectra of carbon, nitrogen and oxygen nuclei for incident neutrons in the thermal to 5 MeV range. In the nuclear arms-control arena, a device that can collect neutron spectral information without revealing design information would have considerable value for treaty verification. Conventional neutron spectrometers operate on a time-of-flight (TOF) basis. Neutrons of interest range in energy from thermal energy (0.025 eV) to a few MeV for special nuclear material and from ca. 100 KeV to 5 MeV for identification of explosives. A thermal neutron has a speed of ca. 2,000 mis; a 1 MeV neutron has a speed of ca. 13,000 km/sec. A TOF spectrometer has a series of choppers, each turning at different speeds, that pass only those neutrons in a given energy (velocity) range; the velocity cohort that is allowed to pass through the spectrometer and be counted is selected by varying the relative speeds ofrotation. Thus, the TOF spectrometer is, by necessity, large (meters to tens of meters). In addition, only a small fraction of all the incident neutrons are measured during any given time interval. That is, the TOF spectrometer makes very inefficient use of the neutron flux. We will describe a spectrometer that has been made practical by the development of neutron-sensitive scintillating fibers. 1-s This concept is "work-in-progress" but the results of a simple theoretical test are reported here.