We have performed x-ray two-photon photoelectron spectroscopy using the Linac Coherent Light Source x-ray free-electron laser in order to study double core-hole (DCH) states of CO2, N2O, and N2. The experiment verifies the theory behind the chemical sensitivity of two-site DCH states by comparing a set of small molecules with respect to the energy shift of the two-site DCH state and by extracting the relevant parameters from this shift.