Thanks to the remarkable ALMA capabilities and the unique configuration of the Cosmic Snake galaxy behind a massive galaxy cluster, we could resolve molecular clouds down to 30 pc linear physical scales in a typical Milky Way progenitor at z = 1.036, through CO(4–3) observations performed at the ∼ 0.2″ angular resolution. We identified 17 individual giant molecular clouds. These high-redshift molecular clouds are clearly different from their local analogues, with 10–100 times higher masses, densities, and internal turbulence. They are offset from the Larson scaling relations. We argue that the molecular cloud physical properties are dependent on the ambient interstellar conditions particular to the host galaxy. We find these high-redshift clouds in virial equilibrium, and derive, for the first time, the CO-to-H2 conversion factor from the kinematics of independent molecular clouds at z = 1. The measured large clouds gas masses demonstrate the existence of parent gas clouds with masses high enough to allow the in-situ formation of similarly massive stellar clumps seen in the Cosmic Snake galaxy in comparable numbers. Our results support the formation of molecular clouds by fragmentation of turbulent galactic gas disks, which then become the stellar clumps observed in distant galaxies.