  In the framework of kt-factorization approach,the production of prompt $\chi_c$ mesons in pp collisions at the LHC energies is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses $g^*g^*\to\chi_{cJ}$ and non-relativistic QCD formalism for bound states. The transverse momentum dependent (unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. Taking into account both color singlet and color octet contributions, we deduce the corresponding non-perturbative long-distance matrix elements from the fits to the latest ATLAS data on $\chi_{c1}$ and $\chi_{c2}$ transverse momentum distributions at $\sqrt s = 7$ TeV. We find that these distributions at small and moderate pt are formed mainly by the color singlet components. We successfully described the data on the differential cross sections and relative production rates $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ presented by the ATLAS, CMS and LHCb Collaborations. We find that the fit points to unequal wave functions of $\chi_{c1}$ and $\chi_{c2}$ states. 
Prompt charmonia production and polarization at LHC in the NRQCD with   kt-factorization. Part II: $\chi_c$ mesons