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We report well-dated Late Cretaceous and Early Tertiary precessional climatic cycles, recorded by rhythmic carbonate maxima and minima in South Atlantic deep sea sites. Spectral analyses of digitized sediment color, a suitable carbonate proxy, show prominent regularities in the spacing marl-carbonate beds. Magnetostratigraphic dating over a number of magnetic chrons constrains the duration of the cycles, which can be detected over at least 20 Myr of sedimentation at 7 coring locations. Their mean absolute period of 23.5 +/- 4.4kyr agrees closely with the predicted late Cretaceous precessional period of 20.8 kyr. Because they can be matched to a physical forcing mechanism with a known repeat time, the cycles offer a new high-resolution tool to measure rates of climate change before and after the Cretaceous-Tertiary (K/T) boundary. From counts of carbonate cycles, we derive the position of the K/T boundary within C29R at 350 kyr after the base of the reversal. The constancy of cycle thickness (linearly related to sedimentation rate) and amplitude up to the "boundary clay" does not give evidence for climate instability preceding the boundary. Orbital chronometry records a step-function decrease in sediment accumulation rate at the Cretaceous-Tertiary boundary that is consistent with a geologically instantaneous event.