We present results from a Chandra study of ultraluminous X-ray sources (ULXs) in a sample of 17 nearby (D_L<60 Mpc) luminous infrared galaxies (LIRGs), selected to have star formation rates (SFRs) in excess of 7 M_sun yr^-1 and low foreground Galactic column densities (N_H < 5*10^20 cm^-2). A total of 53 ULXs were detected and we confirm that this is a complete catalogue of ULXs for the LIRG sample. We examine the evolution of ULX spectra with luminosity by stacking the spectra of individual objects in three luminosity bins, finding a distinct change in spectral index at luminosity ~2 *10^39 erg s^-1. This may be a change in spectrum as 10 M_sun black holes transit from a ~Eddington to a super-Eddington accretion regime, and is supported by a plausible detection of partially-ionised absorption imprinted on the spectrum of the luminous ULX (L_X ~5*10^39 erg s^-1) CXOU J024238.9-000055 in NGC 1068, consistent with the highly ionised massive wind that we would expect to see driven by a super-Eddington accretion flow. This sample shows a large deficit in the number of ULXs detected per unit SFR (0.2 ULXs M_sun^-1 yr^-1). This deficit also manifests itself as a lower differential X-ray luminosity function normalisation for the LIRG sample than for samples of other star forming galaxies. We show that it is unlikely that this deficit is a purely observational effect. Part of this deficit might be attributable to the high metallicity of the LIRGs impeding the production efficiency of ULXs and/or a lag between the star formation starting and the production of ULXs; however, we argue that the evidence -- including very low N_ULX/L_FIR, and an even lower ULX incidence in the central regions of the LIRGs -- shows that the main culprit for this deficit is likely to be the high column of gas and dust in these galaxies, that fuels the high SFR but also acts to obscure many ULXs from our view.
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