The solar nebula carried a strong magnetic field that had a stable intensity and direction for periods of a thousand years or more1. The solar nebular field may have produced post-accretional magnetization in at least two groups of meteorites, CM and CV chondrites 1–3, which originated from planetesimals that may have underwent aqueous alteration before gas in the solar nebula dissipated 1,3. Magnetic minerals produced during aqueous alteration, such as magnetite and pyrrhotite 4, could acquire a chemical remanent magnetization from that nebular field 3. However, many questions about the size, composition, formation time, and, ultimately, identity of the parent bodies that produced magnetized CM and CV chondrites await answers—including whether a parent body might exhibit a detectable magnetic field today. Here, we use thermal evolution models to show that planetesimals that formed between a few Myr after CAIs and ~1 Myr before the nebular gas dissipated could acquire from the nebular field, and retain until today, a chemical remanent magnetization throughout nearly their entire volume. Hence, in-situ magnetometer measurements of C-type asteroids could help link magnetized asteroids to magnetized meteorites. Specifically, a future mission could search for a magnetic field as part of testing the hypothesis that 2 Pallas is the parent body of the CM chondrites 5. Overall, large carbonaceous asteroids might record ancient magnetic fields in magnetic remanence that produces strong modern magnetic fields, even without a metallic core that once hosted a dynamo.