The hyperfine structure (hfs) interaction between the metastable 2 3SI and 2 1S 0 states in 6, 7Li+ causes very small equal and opposite energy level shifts, c~, in the two levels having the same total angular momentum quantum number F=I. This amounts to 12 ppm with respect to the total hfs splitting of 30 GHz for the 7Li+ 2 3S 1 state and has been measured for the first time directly for the case of a core-free electronic system by combined laser-microwave spectroscopy. A new calculation of 6 with accurate integraltransform 2 1S o and 2 3S1 wave functions is reported. Configuration interactions and electron exchange and correlation effects, which differ for parallel (3S~) and antiparallel (1So) spins, are treated in detail in order to obtain very good agreement between measured and theoretical values for this tiny perturbation. A complete understanding of 3 is indispensable for extracting fundamental constants from two-electron spectroscopic data.