Description: High-resolution stable carbon isotope records for upper Paleocene - lower Eocene sections at Ocean Drilling Program Sites 1051 and 690 and Deep Sea Drilling Project Sites 550 and 577 show numerous rapid (40 - 60 kyr duration) negative excursions of up to 1 per mill. We demonstrate that these transient decreases are the expected result of nonlinear insolation forcing of the carbon cycle in the context of a long carbon residence time. The transients occur at maxima in Earth's orbital eccentricity, which result in high-amplitude variations in insolation due to forcing by climatic precession. The construction of accurate orbital chronologies for geologic sections older than ~ 35 Ma relies on identifying a high-fidelity recorder of variations in Earth's orbital eccentricity. We use the carbon isotope records as such a recorder, establishing a robust orbitally tuned chronology for latest Paleocene-earliest Eocene events. Moreover, the transient decreases provide a means of precise correlation among the four sites that is independent of magnetostratigraphic and biostratigraphic data at the 〈10^5-year scale. While the eccentricity-controlled transient decreases bear some resemblance to the much larger-amplitude carbon isotope excursion (CIE) that marks the Paleocene/Eocene boundary, the latter event is found to occur near a minimum in the ~400-kyr eccentricity cycle. Thus the CIE occurred during a time of minimal variability in insolation, the dominant mechanism for forcing climate change on 104-year scales. We argue that this is inconsistent with mechanisms that rely on a threshold climate event to trigger the Paleocene/Eocene thermal maximum since any threshold would more likely be crossed during a period of high-amplitude climate variations.