X-ray photoemission spectroscopy (XPS) provides direct information on atomic composition and stoichiometry by measuring core-electron binding energies. Moreover, from the shift of the binding energy, the so-called chemical shift, the precise chemical type of bonds can be inferred, which brings additional information on the local structure. In this work, we present a theoretical study of the chemical shift first by comparing different theories, from Hartree-Fock and density functional theory to many-body perturbation theory approaches like the GW approximation and its static version (COHSEX). The accuracy of each theory is assessed with respect to a carbon 1s chemical shift experimental benchmark measured on a set of gas-phase molecules. More importantly, by decomposing the chemical shift into different contributions according to terms in the total Hamiltonian, classical electrostatics is identified as the major contributor to the chemical shift, one order of magnitude larger than the correlation.