Polycrystalline CrO₂ is shown to exhibit a giant magnetoresistance (GMR) at low temperatures. A rapid decrease in the GMR with increasing temperature is correlated with a decrease in the intergranular resistance. Single-crystal CrO₂ is a half-metallic ferromagnet, as the data are interpreted to reflect two types of charge carriers, crossing a grain boundary: those that tunnel between conduction bands of adjacent grains and those that hop after residing at a localized state for a time long compared to a spin relaxation time.