Abyssal peridotites are normally thought to be residues of melting of the mid-ocean ridge basalt (MORB) source and are presumably a record of processes affecting the upper mantle. Samples from a single section of abyssal peridotite from the Kane Transform area in the Atlantic Ocean were examined for 190Pt-186Os and 187Re-187Os systematics. They have uniform 186Os/188Os ratios with a mean of 0.1198353 +/- 7, identical to the mean of 0.1198340 +/-12 for Os-Ir alloys and chromitites believed to be representative of the upper mantle. While the Pt/Os ratios of the upper mantle may be affected locally by magmatic processes, these data show that the Pt/Os ratio for the bulk upper mantle has not deviated by more than about +/- 30% from a chondritic Pt/Os ratio over 4.5 billion years. These observations are consistent with the addition of a chondritic late veneer after core separation as the primary control on the highly siderophile element budget of the terrestrial upper mantle. The 187Os/188Os of the samples range from 0.12267 to 0.12760 and correlate well with Pt and Pt/Os, but not Re/Os. These relationships may be explained by variable amounts of partial melting with changing D(Re), reflecting in part garnet in the residue, with a model-dependent melting age between about 600 and 1700 Ma. A model where the correlation between Pt/Os and 187Os/188Os results from multiple ancient melting events, in mantle peridotites that were later juxtaposed by convection, is also consistent with these data. This melting event or events are evidently unrelated to recent melting under mid-ocean ridges, because recent melting would have disturbed the relationship between Pt/Os and 187Os/188Os. Instead, this section of abyssal peridotite may be a block of refractory mantle that remained isolated from the convecting portions of the upper mantle for 600 Ma to >1 Ga. Alternatively, Pt and Os may have been sequestered during more recent melting and possibly melt/rock reaction processes, thereby preserving an ancient melting history. If representative of other abyssal peridotites, then the rocks from this suite with subchondritic 187Os/188Os are not simple residues of recent MORB source melting at ridges, but instead have a more complex history. This suite of variably depleted samples projects to an undepleted present-day Pt/Os of about 2.2 and 187Os/188Os of about 0.128-0.129, consistent with estimates for the primitive upper mantle.