We report an NMR study of the indirect nuclear exchange coupling, electronic structure, and wave-functions overlap in the single crystal of semiconductor TlSe which has a chain structure and comprises two kinds of Tl atoms, Tl1+ and Tl3+. Strong exchange coupling among the spins of Tl1+ and Tl3+ ions, which reside in neighboring chains, is observed. This interaction is significantly stronger than the exchange coupling of the equivalent atoms within the chains. Such an interchain coupling is realized due to the overlap of the Tl1+ and Tl3+ electron wave functions across the intervening Se atom. The aforementioned wave-function overlap is the dominant mechanism in the formation the uppermost valence bands and lower conduction bands in TlSe and determines the electronic structure and the main properties of the compound.