Oscillator strengths for selected transitions of Sr II and Y III have been determined using ab initio multiconfiguration Hartree-Fock techniques. The importance of including an accurate treatment of the core-valence correlation is emphasized. The results are used to determine the abundances of Sr and Y in the chemically peculiar star chi Lupi from HST/GHRS Echelle spectra. Overabundances of 2.09 dex for Sr and 2.8 dex for Y relative to the solar abundance are derived, and an ionization imbalance of +1.1 dex is evident from abundance determinations using Y III and Y II