We demonstrate that the thermodynamic properties of a single liquid aerosol droplet can be explored through the combination of a single-beam gradient force optical trap with Raman spectroscopy. A single aqueous droplet, 2-6 mu m in radius, can be trapped in air indefinitely and the response of the particle to variations in relative humidity investigated. The Raman spectrum provides a unique fingerprint of droplet composition, temperature, and size. Spontaneous Raman scattering is shown to be consistent with that from a bulk phase sample, with the shape of the OH stretching band dependent on the concentration of sodium chloride in the aqueous phase and on the polarization of the scattered light. Stimulated Raman scattering at wavelengths commensurate with whispering gallery modes is demonstrated to provide a method for determining the size of the trapped droplet with nanometer precision and with a time resolution of 1 s. The polarization dependence of the stimulated scatter is consistent with the dependence observed for the spontaneous scatter from the droplet. By characterizing the spontaneous and stimulated Raman scattering from the droplet, we demonstrate that it is possible to measure the equilibrium size and composition of an aqueous droplet with variation in relative humidity. For this benchmark study we investigate the variation in equilibrium size with relative humidity for a simple binary sodium chloride/aqueous aerosol, a typical representative inorganic/aqueous aerosol that has been studied extensively in the literature. The measured equilibrium sizes are shown to be in excellent agreement with the predictions of Kohler theory. We suggest that this approach could provide an important new strategy for characterizing the thermodynamic properties and kinetics of transformation of aerosol particles.