The isotopic composition of helium in cosmic ray fluxes provides valuable information about cosmic ray propagation through the Galaxy, which is of particular interest to indirect dark matter searches. Helium-3, mainly a secondary cosmic ray species, is primarily produced by spallation of heavier cosmic rays, such as primary helium-4, with interstellar matter. In six years of data taking, AMS has collected the largest available data set on fluxes of cosmic-ray helium. Events are selected to form a clean sample of galactic helium nuclei, for which velocity and rigidity give a measurement of particle mass that allows the measurement of relative isotope abundances. The resolution of measured mass is described in detail by template functions based on the underlying resolutions of the silicon tracker and ring-imaging Cerenkov detector measurements. This thesis presents a measurement of the cosmic ray helium isotope ratio 3He/4He in the range 0.8-10 GeV/nucleon, as obtained through a template fitting approach on AMS data. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - docs mit.edu).