The excess of highly siderophile (iron-loving) elements (HSEs) and the chondritic ratios of most HSEs in the bulk silicate Earth (BSE) may reflect the accretion of a chondritic 'late veneer' of about 0.5 per cent of Earth's mass after core formation. The amount of volatiles contained in the late veneer is a key constraint on the budget and the origin of the volatiles in Earth. At high pressures and temperatures, the moderately volatile chalcogen elements sulphur (S), selenium (Se) and tellurium (Te) are moderately to highly siderophile; thus, if depleted by core formation their mantle abundances should reflect the volatile composition of the late veneer. Here we report ratios and abundances of S, Se and Te in the mantle determined from new isotope dilution data for post-Archaean mantle peridotites. The mean S/Se and Se/Te ratios of mantle lherzolites overlap with CI (Ivuna-type) carbonaceous chondrite values. The Se/Te ratios of ordinary and enstatite chondrites are significantly different. The chalcogen/HSE ratio of the BSE is similar to that of CM (Mighei-type) carbonaceous chondrites, consistent with the view that the HSE signature of the BSE reflects a predominance of slightly volatile-depleted, carbonaceous-chondrite-like material, possibly with a minor proportion of non-chondritic material. Depending on the estimates for the abundances of water and carbon in the BSE, the late veneer may have supplied 20 to 100 per cent of the budget of hydrogen and carbon in the BSE.