The disc structure of the Milky Way is marked by a chemical dichotomy, with high-alpha and low-alpha abundance sequences, traditionally identified with the geometric thick and thin discs. This identification is aided by the old ages of the high-alpha stars, and lower average ages of the low-alpha ones. Recent large scale surveys such as APOGEE have provided a wealth of data on this chemical structure, including showing that an identification of chemical and geometric thick discs is not exact, but the origin of the chemical dichotomy has remained unclear. Here we demonstrate that a dichotomy arises naturally if the early gas-rich disc fragments, leading to some fraction of the star formation occurring in clumps of the type observed in high-redshift galaxies. These clumps have high star formation rate density. They, therefore, enrich rapidly, moving from the low-alpha to the high-alpha sequence, while more distributed star formation produces the low-alpha sequence. We demonstrate that this model produces a chemically-defined thick disc that has many of the properties of the Milky Ways thick disc. Because clump formation is common in high redshift galaxies, we predict that chemical bimodalities are common in massive galaxies.