Insoluble organic matter (IOM) in primitive carbonaceous meteorites has preserved its chemical composition and isotopic heterogeneity since the solar system formed ~4.567 billion years ago. We have identified the carrier moieties of isotopically anomalous hydrogen in IOM isolated from the Orgueil carbonaceous chondrite. Data from high spatial resolution, quantitative isotopic NanoSIMS mapping of Orgueil IOM combined with data from electron paramagnetic resonance spectroscopy reveals that organic radicals hold all the deuterium excess (relative to the bulk IOM) in distinct, micrometer-sized, D-rich hotspots. Taken together with previous work, the results indicate that an isotopic exchange reaction took place between pre-existing organic compounds characterized by low D/H ratios and D-rich gaseous molecules, such as H₂D⁺ or HD₂ ⁺. This exchange reaction most likely took place in the diffuse outer regions of the proto-planetary disk around the young Sun, offering a model that reconciles meteoritic and cometary isotopic compositions of organic molecules.