The geochemical composition of the Earth's upper mantle(1-3) is thought to reflect 4.5 billion years of melt extraction, as well as the recycling of crustal materials. The fractionation of rhenium and osmium during partial melting in the upper mantle makes the Re-Os isotopic system well suited for tracing the extraction of melt and recycling of the resulting mid-ocean-ridge basalt(3). Here we report osmium isotope compositions of more than 700 osmium-rich platinum-group element alloys derived from the upper mantle. The osmium isotopic data form a wide, essentially gaussian distribution, demonstrating that, with respect to Re-Os isotope systematics, the upper mantle is extremely heterogeneous. As depleted and enriched domains can apparently remain unequilibrated on a timescale of billions of years, effective equilibration seems to require high degrees of partial melting, such as occur under mid-ocean ridges or in back-arc settings, where percolating melts enhance the mobility of both osmium and rhenium. We infer that the gaussian shape of the osmium isotope distribution is the signature of a random mixing process between depleted and enriched domains, resulting from a 'plum pudding' distribution in the upper mantle, rather than from individual melt depletion events.