The ratio of natural remanence (NRM) to saturation remanence (IRMs) is found to be exceedingly high for a number of basaltic to ultramafic samples from the 3.4 billion year old Barberton Mountain Land greenstone belt, South Africa. Although conventional paleointensity methods indicate paleofields of several oersteds, demagnetization curves plotted on logarithmic scale clearly show the NRM in these samples to be unlike thermal remanence (TRM). It seems most probable that the observed NRM is a chemical remanence (CRM) related to the greenschist metamorphic event, and that the intense magnetizations are perhaps the result of internally generated, rather than external fields. The probability that the intense magnetization observed in these ancient terrestrial samples is unrelated to the strength of the external field suggests caution in the interpretation of paleointensity results from extraterrestrial materials.