The determination of elemental abundances plays an important role inunderstanding the atmospheric processes that lead to anomalies inspectra of chemically peculiar stars. Ongoing study of the HgMn star χ Lupi has defined much of the elemental abundance distribution but progress is dependent upon the availability and accuracy of the atomic data. Here we present experimentally determined wavelengths and oscillator strengths for 27 Os II and 23 Ir II transitions. The oscillator strengths have been determined by combining radiative lifetimes measured using the laser-induced fluorescence technique withbranching fractions determined from Fourier transform spectrometeremission line intensities. The new data were used in a synthetic spectrum analysis of high-resolution ultraviolet spectra of χ Lupi obtained with the Hubble Space Telescope. Weak abundance enhancement swere determined for both elements, Os/H = +1.3 dex and Ir/H = +0.7dex, which now clearly defines the heavy element abundance peak in this star to be comprised of only the four elements Pt, Au, Hg, and Tl. This result offers a new constraint on theoretical efforts to explain the observed spectrum anomalies. Based in part on observations obtained with the GHRS instrument on board the Hubble Space Telescope.