The structural, electronic and optical properties of CuBX₂ (X = S, Se, Te) chalcopyrite semiconductors have been studied using the full-potential (linearized) augmented plane-wave (FP(L)APW) method based on the density functional theory (DFT) within the Yukawa screened-PBE0 (YS-PBE0) hybrid functional as implemented in the WIEN2k package. We have found that our calculated structural and electronic parameters such as lattice parameter, tetragonal ratio, anion displacement and energy band gap are in very good agreement with previous experimental results. We have also presented the real and imaginary parts of the dielectric function, refractive index and absorption coefficients to describe optical properties of the investigated chalcopyrite semiconductors. Furthermore, the phonon dispersion curves and corresponding density of states have been studied by using a linear response approach based on the density functional perturbation theory implemented in the Quantum ESPRESSO code. Finally, transport properties such as the Seebeck coefficient, thermal and electrical conductivity and the figure of merit for these materials have been calculated using the semi-classical Boltzmann theory as implemented in the BoltzTraP code.