For many years, detailed observational and statistical study of chemically peculiar stars has shown that the overabundance of heavy radioactive chemical elements in their atmospheres is not well understood. We try to explain the overabundance of a few of them by the explosion of possible supernovae in binary or multiple-stellar systems, i.e., to search for a chemically peculiar star and pulsar pair by traceback motion study in the galaxy. We analyzed trajectories of 529 chemically peculiar stars in our sample and 28 pulsars from the ATNF catalogue, with ages that do not exceed 100 Myr, and obtained several possible candidate pairs (CP star plus pulsar), which may have been at the same place at the same time. Moreover, our traceback study of them with the young stellar clusters (Hunt and Reffert, 2023) led to the identification of several possibly parental stellar groups. However, more detailed studies are needed to estimate the ages of chemically peculiar stars and detect their locations of formation, as well as using statistical methods to assess whether the possible supernova ejection is the result of coincidence or not. Obviously, modeling of the best chemically peculiar star–pulsar pairs will also allow us to explain the processes occurring in these stars.