We examine whether the super star-forming clumps (R~1-3 kpc; M~10^8-10^9.5 Msun) now known to be a key component of star-forming galaxies at z~2 could be the formation sites of the locally observed old globular cluster population. We find that the stellar populations of these super star-forming clumps are excellent matches to those of local metal-rich globular clusters. Moreover, this globular cluster population is known to be associated with the bulges / thick disks of galaxies, and we show that its spatial distribution and kinematics are consistent with the current understanding of the assembly of bulges and thick disks from super star-forming clumps at high redshift. Finally, with the assumption that star formation in these clumps proceeds as a scaled-up version of local star formation in molecular clouds, this formation scenario reproduces the observed numbers and mass spectra of metal-rich globular clusters. The resulting link between the turbulent and clumpy disks observed in high-redshift galaxies and a local globular cluster population provides a plausible co-evolutionary scenario for several of the major components of a galaxy: the bulge, the thick disk, and one of the globular cluster populations.