The cold molecular gas in contemporary galaxies is structured in discrete cloud complexes. These giant molecular clouds (GMCs), with 104–107 solar masses (M⊙) and radii of 5–100 parsecs, are the seeds of star formation1. Highlighting the molecular gas structure at such small scales in distant galaxies is observationally challenging. Only a handful of molecular clouds were reported in two extreme submillimetre galaxies at high redshift2,3,4. Here we search for GMCs in a typical Milky Way progenitor at z = 1.036. Using the Atacama Large Millimeter/submillimeter Array (ALMA), we mapped the CO(4–3) emission of this gravitationally lensed galaxy at high resolution, reading down to 30 parsecs, which is comparable to the resolution of CO observations of nearby galaxies5. We identify 17 molecular clouds, characterized by masses, surface densities and supersonic turbulence all of which are 10–100 times higher than present-day analogues. These properties question the universality of GMCs6 and suggest that GMCs inherit their properties from ambient interstellar medium. The measured cloud gas masses are similar to the masses of stellar clumps seen in the galaxy in comparable numbers7. This corroborates the formation of molecular clouds by fragmentation of distant turbulent galactic gas disks8,9, which then turn into stellar clumps ubiquitously observed in galaxies at ‘cosmic noon’ (ref. 10).