A Thomson scattering spectrometer was developed to measure the electron velocity distribution function (EDF) in a localized volume of plasma by angularly and spectrally resolving the Thomson scattered light. In the collective regime, scattering from electron plasma waves becomes efficient over a narrow range of frequencies when k-matching conditions between the experimental geometry and plasma parameters are satisfied. By resolving the continuum of Thomson scattered light as a function of angle, a span of plasma k-vectors are sampled. Each corresponding spectrum is sensitive to a different part of the EDF. Light collection is accomplished using an off-axis, cylindrical segment of a modified Schwarzschild telescope. The collection aperture spans 120° (N.A. 0.86) in the angularly resolved axis and 12° (N.A. 0.10) in the orthogonal axis. A cylindrical lens focuses the orthogonal rays to generate a line image that is coupled to a grating spectrometer. The spectrally dispersed image is recorded with a time-gated-intensified-camera. The information contained in ensemble of Thomson scattered spectra are used to determine the shape of the EDF, with no assumption to form, with over four orders of magnitude of dynamic range.