The nearest region of massive star formation - the Scorpius-Centaurus OB2 association (Sco-Cen) - is a local laboratory ideally suited to the study of a wide range of astrophysical phenomena. Precision astrometry from the Gaia mission has expanded the census of this region by an order of magnitude. However, Sco-Cen's vastness and complex substructure make kinematic analysis of its traditional three regions, Upper Scorpius, Upper Centaurus-Lupus, and Lower Centaurus-Crux, challenging. Here, we use CHRONOSTAR, a Bayesian tool for kinematic age determination, to carry out a new kinematic decomposition of Sco-Cen using full six-dimensional kinematic data. Our model identifies eight kinematically distinct components consisting of 8185 stars distributed in dense and diffuse groups, each with an independently fit kinematic age; we verify that these kinematic estimates are consistent with isochronal ages for K dwarfs. Both Upper Centaurus-Lupus and Lower Centaurus-Crux are split into two parts. The kinematic age of the component that includes PDS 70, one of the most well-studied systems currently forming planets, is 15 ± 3 Myr.