Absorption spectra of Tl+-doped KMgF3 single crystals have been measured at various temperatures between 9 and 300 K in the V.u.v. region. Three main bands are found, and they are labelled A, B, C in order of increasing energy because of their close similarities to those of Tl+ ions in alkali halides. The most striking novelty in KMgF3:Tl+ is given by the clearly resolved structures of the A and C bands, which both exhibit three components at all temperatures. These structures are related to the Jahn-Teller splitting, due to the interaction of the impurity ion with non-cubic lattice vibrations, and to a static distortion of the host lattice.