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The variation of delta(18)O that results from nearly all physical, biological and chemical processes on the Earth is approximately twice as large as the variation of delta(17)O. This so-called ’mass-dependent’ fractionation is well documented in terrestrial minerals(1,2). Evidence for ’mass- independent’ fractionation (Delta(17)O = delta(17)O-0.52 delta(18)O), where deviation from this tight relationship occurs, has so far been found only in meteoritic material and a few terrestrial atmospheric substances(3). In the rock record it is thought that oxygen isotopes have followed a mass-dependent relationship for at least the past 3.7 billion years (ref. 4), and no exception to this has been encountered for terrestrial solids(5). Here, however, we report oxygen-isotope values of two massive sulphate mineral deposits, which formed in surface environments on the Earth but show large isotopic anomalies (Delta(17)O up to 4.6 parts per thousand). These massive sulphate deposits are gypcretes from the central Namib Desert and the sulphate-bearing Miocene volcanic ash-beds in North America. The source of this isotope anomaly might be related to sulphur oxidation reactions in the atmosphere and therefore enable tracing of such oxidation. These findings also support the possibility of a chemical origin of variable isotope anomalies on other planets, such as Mars(6).