We have recently shown that a template-associated protein kinase, which phosphorylates the carboxyl-terminal domain (CTD) of RNA polymerase II, is a two-component system. We describe here the purification of these two components to apparent homogeneity from human (HeLa) cell nuclear extract. Kinase component A has a 340-kDa native molecular mass, consists of a single large polypeptide, and contains the kinase active site. Kinase component B, which is identical to the Ku autoantigen, has a 180-kDa native molecular mass, and consists of apparently equimolar 67- and 83-kDa polypeptides. Component B stimulates the activity of component A, and under some conditions, confers DNA dependence on the reaction. The purified kinase converts the CTD to the multiply phosphorylated CTD0 form. Conversion occurs processively, and this processivity is an inherent property of component A. The in vitro phosphorylated CTD0 form contains approximately equimolar phosphoserine and phosphothreonine, but no detectable phosphotyrosine.