While the onset of plate tectonics has been proposed as far back in time as the Hadean, there is no evidence for rigid crust that can accommodate linear dyke swarms until ca 2700 Ma in the Pilbara Craton, and at ca 2500 Ma in most other Archean cratons. Here, we provide a precise 3317.0 ± 1.1 Ma baddeleyite U–Pb ID-TIMS age determination for a dolerite from a regionally extensive dyke swarm underlying the Euro Basalt in the East Pilbara Terrane, with links to the Kaapvaal Craton that would establish it as part of what may be the oldest large igneous provinces on Earth. We link this event to the deposition of large volcano-sedimentary basins, reflecting the brittle fracturing that enables emplacement of the dyke swarm and the overlying thick succession of mafic-to-ultramafic lavas. This is the first time that a dyke swarm has been used as evidence for rigid crust prior to 3000 Ma, suggesting that lithospheric conditions appropriate for some form of plate tectonics existed at least as far back as the Paleoarchean. KEY POINTS We provide a precise 3317.0 ± 1.1 Ma baddeleyite U–Pb ID-TIMS age determination for a dolerite in the Pilbara Craton. The dated dyke is part of the potentially oldest large igneous province on Earth. The dolerite dyke swarm was emplaced into rigid crust at ca 3.32 Ga. Lithospheric conditions that accommodated plate tectonics existed as least as far back as the Paleoarchean.