The paper presents the X-ray photoelectron spectra (XPS) of the valence band (VB) and of the principal core levels (CL) from the (010) and (001) plane axes for the quasi-one-dimensional TlInSe2 single crystal. The XPS were measured with monochromatized Al Kα radiation in the energy range of 0-1400 eV at room and 393 K temperature. The VB is located 0.6-10 eV below the Fermi level. Experimental energies of the VB and CL are compared with the results of quantum mechanical ab initio calculations of the molecular model of the TlInSe2 crystal. The electronic structure of the VB and CL is described theoretically by quantum mechanical Hartree-Fock calculations. The surface and bulk atoms influence the shape of the VB and CL, which is crystallographic plane dependent. The chemical shifts in the TlInSe2 crystal for the Tl, In, and Se states are obtained.