We report an unexpected anomaly in the zero-field Hall coefficient of two-dimensional electron systems in high-mobility GaAs/AlGaAs heterostructures. Our device layout allows the investigation of mesoscopic systems with variable Fermi energy as well as with tunable Hall probes. At very low temperature, both positive and negative deviations from the noninteracting Hall coefficient ␥ H 0 are observed, which can be twice as large as ␥ H 0 itself. A distinct regularity in the deviations and their temperature dependence are interpreted as the spontaneous formation of localized spins and their indirect exchange interaction.