A 13-million-year continuous record of Oligocene climate from the equatorial Pacific reveals a pronounced "heartbeat" in the global carbon cycle and periodicity of glaciations. This heartbeat consists of 405,000-, 127,000-, and 96,000-year eccentricity cycles and 1.2-million-year obliquity cycles in periodically recurring glacial and carbon cycle events. That climate system response to intricate orbital variations suggests a fundamental interaction of the carbon cycle, solar forcing, and glacial events. Box modeling shows that the interaction of the carbon cycle and solar forcing modulates deep ocean acidity as well as the production and burial of global biomass. The pronounced 405,000-year eccentricity cycle is amplified by the long residence time of carbon in the oceans.