A simple, selective and sensitive fluorescence quenching method was developed to the determination Cr(VI). The method is based on the oxidation of $I^-;to;{{I_3}^-}$ by Cr(VI) in sulfuric acid solution followed by immediate formation of ion association compound between I3 ? and rhodamine 6G in Tween-80 micellar media at room temperature. The influence of several surfactants on rhodamine 6G fluorescence signal was studied; particular attention was paid in the aggregation behavior of rhodamine 6G?Tween-80 system. The experimental parameters (e.g., type of surfactant, reagent concentration) were studied and the optimal conditions were established. The linear calibration graph was obtained in the range 2.0 - 100.0 ng m$L^{-1}$ Cr(VI). The detection limit of the method was 0.37 ng m$L^{-1}$. The relative standard deviation (R.S.D.) is less than 5% (n = 5). The efficiency of the method for the determination of Cr(VI) in the presence of Cr(III) in the sample was investigated. The method was applied successfully to the determination of Cr(VI) and total Cr in water, and liver tissue samples.