The solubility of rhenium (Re) in a haplobasaltic melt (anorthite-diopside eutectic composition) has been experimentally determined using the mechanically assisted equilibration technique at 1400°C as a function of oxygen fugacity (10-12 < fO2 ≤ 10-7 bar), imposed by CO-CO2 gas mixtures. Samples were analysed by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). This is a true microanalytical technique, which allows small-scale sample heterogeneity to be detected, while providing a limit of detection of 2 ppb Re. Time-resolved LA-ICP-MS spectra revealed the presence of suboptically sized micronuggets of Re in all samples, which, because they are present at the 0.5 to 10 ppm level, dominate the true solubilities of Re (<1 ppm at the conditions of the experiment) in bulk analyses of the samples. Nevertheless, the micronuggets could be filtered out from the time-resolved spectra to reveal accurate values of the true Re solubility. A number of time series of samples were taken at constant fO2 to demonstrate that the solubilities converge to a constant value. In addition, solubilities were measured after increasing and decreasing the imposed fO2. The results show that Re dissolves in the silicate melt as ReO2 (Re4+) and ReO3 (Re6+) species, with the latter predominating at typical terrestrial upper-mantle oxygen fugacities. The total solubility of Re is described by the following expression (fO2 in bars): [Re/ppb] = 9.7(±1.9) × 109 (fO2) + 4.2 (±0.3) × 1014 (fO2)1.5 Assuming an activity coefficient for Re in Fe-rich metal of 1, this gives a value of Dmet/silRe of 5 × 1010 at log fO2 = IW-2, appropriate for metal-silicate partitioning in an homogenously accreting Earth. Thus, Re is indeed very highly siderophile, and the mantle's abundance cannot be explained by homogenous accretion.