Astronomical calculations reveal the Solar System's dynamical evolution, including its chaoticity, and represent the backbone of cyclostratigraphy and astrochronology. An absolute, fully calibrated astronomical time scale has hitherto been hampered beyond similar to 50 million years before the present (Ma) because orbital calculations disagree before that age. Here, we present geologic data and a new astronomical solution (ZB18a) showing exceptional agreement from similar to 58 to 53 Ma. We provide a new absolute astrochronology up to 58 Ma and a new Paleocene-Eocene boundary age (56.01 +/- 0.05 Ma). We show that the Paleocene-Eocene Thermal Maximum (PETM) onset occurred near a 405-thousand-year (kyr) eccentricity maximum, suggesting an orbital trigger. We also provide an independent PETM duration (170 +/- 30 kyr) from onset to recovery inflection. Our astronomical solution requires a chaotic resonance transition at similar to 50 Ma in the Solar System's fundamental frequencies.