A technique to measure the electrical conductivity of single molecules has been demonstrated. The method is based on trapping molecules between an STM tip and a substrate. The spontaneous attachment and detachment of α,ω-alkanedithiol molecular wires was easily monitored in the time domain. Electrical contact between the target molecule and the gold probes was achieved by the use of thiol groups present at each end of the molecule. Characteristic jumps in the tunnelling current were observed when the tip was positioned at a constant height and the STM feedback loop was disabled. Histograms of the measured current jump values were used to calculate the molecular conductivity as a function of bias and chain length. In addition, it is demonstrated that these measurements can be carried out in a variety of environments, including aqueous electrolytes. The changes in conductivity with chain length obtained are in agreement with previous results obtained using a conducting AFM and the origin of some discrepancies in the literature is analysed.