Layered intrusions represent part of the plumbing systems that deliver vast quantities of magma through the Earth's crust during the formation of large igneous provinces, which disrupt global ecosystems and host most of the Earth's endowment of Pt, Ni and Cr deposits. The Rustenburg Layered Suite of the enormous Bushveld Igneous Complex of South Africa has been presumed to have formed by deposition of crystals at the floor of a subterranean sea of magma several km deep and hundreds of km wide called a magma chamber. Here we show, using U-Pb isotopic dating of zircon and baddeleyite, that individual chromitite layers of the Rustenburg Layered Suite formed within a stack of discrete sheet-like intrusions emplaced and solidified as separate bodies beneath older layers. Our U-Pb ages and modelling necessitate reassessment of the genesis of layered intrusions and their ore deposits, and challenge even the venerable concept of the magma chamber itself.