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‰. 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 <10⁵-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.