Mass-independent (MI) sulfur isotopic anomalies recently observed in Precambrian rock samples have been attributed to photochemistry and used to establish oxygen levels in Earth's early atmosphere <Farquhar et al., 2000b, 2000a>. Here we report the first MI sulfur isotopic compositions in the present atmosphere from samples of Northern Hemispheric aerosol sulfate. The MI sulfur isotopic compositions do not correlate with MI oxygen signatures previously observed in the same samples <Lee and Thiemens, 2001; Lee, 2000; Bao et al., 2001>. Antarctic dry valley soil sulfate, which is atmospheric in origin and has a MI oxygen signature <Bao et al., 2000>, is mass-dependent (MD) with respect to sulfur. A different process than that proposed to explain the MI oxygen signature in sulfate <Savarino et al., 2000> is therefore required. Possible sources of the anomaly are discussed, as well as potential applications to global climate and implications for Archean geology and the Earth's early atmosphere.