Starting from the recent discovery of chlorine ions in Io's plasma torus, we searched for evidence of Cl-bearing species at the surface of the satellite. We have identified Cl2SO2, with possible contribution by ClSO2, as candidates for the absorber(s) of the 3.92 ¿m band locally present in NIMS/Galileo spectra of the reddish deposits south of Marduk's volcanic center. Low-temperature laboratory measurements of the infrared spectra of several Cl and S-bearing molecules in the solid state, coupled with radiative transfer modeling, first allowed us to select four candidate molecules. Their abundance and stability at Io's surface have been tested through formation, condensation, and destruction scenarios using volcanic and atmospheric models completed with chemical and thermodynamical data. In particular, the sublimation rates of solid Cl2SO2 and SO2 have been measured to study the selective condensation of these species. Cl2SO2 diluted at ~1% in a millimeter thick layer of solid SO2 is the favorite candidate for the 3.92 ¿m band. We strongly favor a formation process of this molecule by heterogeneous reaction of Cl atoms on SO2 ice condensing on plume particles or at Io's surface. The high Cl2SO2 abundance observed implies that a Cl-rich volcanic eruption (/S > 0.015) occurred at Marduk. ClSO2 is a potential additional contributor to the band. Pure H2S is safely discarded as it is extremely unstable at Io's surface but an upper limit of 0.01% is derived for H2S diluted in SO2. Finally, chemical constraints allow us to firmly exclude H2S2. We also suggest that Cl2S may be an alternative explanation for the reddish coloration of some volcanic deposits.