We report the fabrication of self-assembled, strain-free GaAs/Al$_{0.27}$Ga$_{0.73}$As quantum dot pairs which are laterally aligned in the growth plane, utilizing the droplet epitaxy technique and the anisotropic surface potentials of the GaAs (100) surface for the migration of Ga adatoms. Photoluminescence spectra from a single quantum dot pair, consisting of a doublet, have been observed. Finite element energy level calculations of a model quantum dot pair are also presented.