We determined the solubility limit of Pt in molten haplo-basalt (1 atm anorthite-diopside eutectic composition) in piston-cylinder and multi-anvil experiments at pressures between 0.5 and 14 GPa and temperatures from 1698 to 2223 K. Experiments were internally buffered at ∼IW + 1. Pt concentrations in quenched-glass samples were measured by laser-ablation inductively coupled-plasma mass spectrometry (LA-ICPMS). This technique allows detection of small-scale heterogeneities in the run products while supplying three-dimensional information about the distribution of Pt in the glass samples. Analytical variations in 195Pt indicate that all experiments contain Pt nanonuggets after quenching. Averages of multiple, time-integrated spot analyses (corresponding to bulk analyses) typically have large standard deviations, and calculated Pt solubilities in silicate melt exhibit no statistically significant covariance with temperature or pressure. In contrast, averages of minimum 195Pt signal levels show less inter-spot variation, and solubility shows significant covariance with pressure and temperature. We interpret these results to mean that nanonuggets are not quench particles, that is, they were not dissolved in the silicate melt, but were part of the equilibrium metal assemblage at run conditions. We assume that the average of minimum measured Pt abundances in multiple probe spots is representative of the actual solubility. The metal/silicate partition coefficients (Dmet/sil) is the inverse of solubility, and we parameterize Dmet/sil in the data set by multivariate regression. The statistically robust regression shows that increasing both pressure and temperature causes Dmet/silto decrease, that is, Pt becomes more soluble in silicate melt. Dmet/sil decreases by less than an order of magnitude at constant temperature from 1 to 14 GPa, whereas isobaric increase in temperature produces a more dramatic effect, with Dmet/sil decreasing by more than one order of magnitude between 1623 and 2223 K. The Pt abundance in the Earth's mantle requires that Dmet/sil is ∼1000 assuming core-mantle equilibration. Geochemical models for core formation in Earth based on moderately and slightly siderophile elements are generally consistent with equilibrium metal segregation at conditions generally in the range of 20-60 GPa and 2000-4000 K. Model extrapolations to these conditions show that the Pt abundance of the mantle can only be matched if oxygen fugacity is high (∼IW) and if Pt mixes ideally in molten iron, both very unlikely conditions. For more realistic values of oxygen fugacity (∼IW - 2) and experimentally-based constraints on non-ideal mixing, models show that Dmet/sil would be several orders of magnitude too high even at the most favorable conditions of pressure and temperature. These results suggest that the mantle Pt budget, and by implication other highly siderophile elements, was added by late addition of a 'late veneer' phase to the accreting proto-Earth.