We report a theoretical study of the selective vibrational excitation of a HCl molecule achieved by Raman chirped adiabatic passage (RCAP) and probed by X-ray photoelectron spectroscopy (XPS). It is demonstrated that HCl can be prepared in any vibrational level up to ν = 9 with nearly complete population inversion. We explore the effects of both the rotation of the molecule and of the temperature on the RCAP process, which is proved to be very robust. Furthermore, we emphasize that XPS spectra at the chlorine K-shell threshold show characteristic signatures of the populated vibrational level, allowing us to follow the RCAP process.