Solid solutions 1T-CrxTi1-xSe2 (x = 0-0,83) were synthesized. Single crystals in the concentration range x = 0-0.69 were grown. Structure of these materials was studied on single- and polycrystalline samples. It was determined that chromium atoms substitute for titanium atoms in the TiSe2 host lattice. XPS measurements of the core levels together with the resonance valence band spectra of the 1T-CrxTi1-xSe2, as well as absorption spectra of Ti and Cr were performed. According to the experimental XAS data and multiplet atomic calculation, titanium and chromium atoms have oxidation numbers of +4 and +3, respectively. The local magnetic moment of about 3 eV is detected at Cr atoms. A transition into the spin glass state is observed. The modeling calculations of chromium local density of states were carried out. These results are in a good agreement with the experimental ones and suggest that 3d density of electronic states of chromium that substitutes for titanium in the host lattice is spin polarized and has a half-metallic character.