Mass-independent fractionation of sulfur isotopes (reported as Delta S-33) recorded in Archean sedimentary rocks helps to constrain the composition of Earth's early atmosphere and the timing of the rise of oxygen similar to 2.4 billion years ago. Although current hypotheses predict uniformly negative Delta S-33 for Archean seawater sulfate, this remains untested through the vast majority of Archean time. We applied x-ray absorption spectroscopy to investigate the low sulfate content of particularly well-preserved Neoarchean carbonates and mass spectrometry to measure their Delta S-33 signatures. We report unexpected, large, widespread positive Delta S-33 values from stratigraphic sections capturing over 70 million years and diverse depositional environments. Combined with the pyrite record, these results show that sulfate does not carry the expected negative Delta S-33 from sulfur mass-independent fractionation in the Neoarchean atmosphere.