The evolutionary origins of the tricarboxylic acid cycle (TCA), or Krebs cycle, are so far unclear. Despite a few years ago, the existence of a simple non-enzymatic Krebs-cycle catalyst has been dismissed 'as an appeal to magic', citrate and other intermediates have meanwhile been discovered on a carbonaceous meteorite and do interconvert non-enzymatically. To identify the non-enzymatic Krebs cycle catalyst, we used combinatorial, quantitative high-throughput metabolomics to systematically screen iron and sulfate reaction milieus that orient on Archean sediment constituents. TCA cycle intermediates are found stable in water and in the presence of most iron and sulfate species, including simple iron-sulfate minerals. However, we report that TCA intermediates undergo 24 interconversion reactions in the presence of sulfate radicals that form from peroxydisulfate. The non-enzymatic reactions critically cover a topology as present in the Krebs cycle, the glyoxylate shunt and the succinic semialdehyde pathways. Assembled in a chemical network, the reactions achieve more than ninety percent carbon recovery. Our results show that a non-enzymatic precursor for the Krebs cycle is biologically sensible, efficient, and forms spontaneously in the presence of sulfate radicals.