Organic materials are promising candidates for integration in optical network components allowing fast communication. Ultimate speeds can be obtained by exploiting third-order nonlinear optical light-matter interactions that ultimately rely on the molecular second hyperpolarizability (γ). The exploration of molecular structure-property relations is crucial to optimize γ but requires state of the art measurement techniques which are both sensitive and efficient. Unfortunately, present-day methods for probing the performance of third-order nonlinear optical (NLO) materials fail to meet at least one of those requirements. We have developed third-harmonic scattering (THS) as an alternative method to measure γ in solution, featuring a simple experimental setup and straightforward data analysis. Since the signal strength relies on |γ|2, the method proves to be very sensitive and allows rapid screening of organic molecules in dilute solutions for potential use in third-order NLO applications. In this manuscript, we demonstrate the experimental procedure and calibration of THS and have determined the second hyperpolarizability |γ| of commonly used solvents, which can be used as an internal calibration standard. As a proof of concept we determined γ of trans-stilbene and found it to be in excellent agreement with values obtained by other techniques.