The binary coalescence of aqueous droplets has been observed in a single-beam gradient-force optical trap. By measuring the time-dependent intensity for elastic scattering of light from the trapping laser, the dynamics of binary coalescence have been examined and the time scale for equilibration of a composite droplet to ambient conditions has been determined. These data are required for modeling the agglomeration of aqueous droplets in dense sprays and atmospheric aerosol. Elastic-light scattering from optically trapped particles has not been used previously to study the time-resolved dynamics of mixing. It is shown to offer a unique opportunity to characterize the binary coalescence of aqueous droplets with radii from 1 to 6 mu m. The study of this size regime, which cannot be achieved by conventional imaging methods, is critical for understanding the interactions of droplets in the environment of dense sprays.