We present an instrument that addresses two critical requirements for quantitative measurements of the homogeneous crystal nucleation rate in supersaturated aqueous solution. First, the need to perform repeated measurements of nucleation incubation times is met by automating experiments to enable programmable cycling of thermodynamic conditions. Second, the need for precise and robust control of the chemical potential in supersaturated aqueous solution is met by implementing a novel technique for regulating relative humidity. The apparatus levitates and weighs micron-sized samples in an electric field, providing access to highly supersaturated states. We report repeated observations of the crystal nucleation incubation time in a supersaturated aqueous sodium chloride droplet, from which we infer the nucleation rate.