ALH84001 is a coarse-grained, elastic orthopyroxenite meteorite related to the SNC meteorite group (shergottites, nakhlites, Chassigny). Superimposed upon the orthopyroxene-dominant igneous mineral assemblage is hydrothermal signature. This hydrothermal overprint consists of carbonate assemblages occurring in spheroidal aggregates and fine-grained carbonate-sulfide vug-filling. The sulfide in this assemblage has been identified as pyrite, an unusual sulfide in meteorites. Previously, Burgess et al. (1989) reported a bulk delta(34)S for a SNC group meteorite (Shergotty) of -0.5 +/- 1.5 parts per thousand. Here, we report the first martian delta(34)S values from individual sulfide grains. Using newly developed ion microprobe techniques, we were able to determine delta(34)S of the pyrite in ALH84001 with a 1 alpha precision of better than +/-0.5 parts per thousand. The delta(34)S values for the pyrite range from +4.8 to +7.8 parts per thousand. Within the stated uncertainties, the pyrite from ALH84001 exhibits a real variability in delta(34)S in this alteration assemblage. In addition, these sulfides are demonstrably enriched in S-34 relative to Canon Diablo troilite and sulfides from most other meteorites. This signature implies that the planetary body represented by ALH84001 experienced processes capable of fractionating sulphur isotopes and that hydrothermal conditions changed during pyrite precipitation (T, pH, fluid composition, etc.). The fractionated signature of the sulphur in the pyrite is most likely attributed to either conditions of pyrite precipitation (low temperature, reduced (low f(o2)) and moderately alkaline (pH > 8) environment) or enrichment of fluids in S-34 by surface processes (weathering or impact processes) prior to precipitation. These new data are not consistent with the pyrite recording either biogenic activity or atmospheric fractionation of sulphur through nonthermal escape mechanisms or oxidation processes. This study also demonstrates the usefulness of ion microprobe measurements of sulphur isotopes in constraining conditions on other planetary bodies.