We report the first study of electrical contact with an individual molecule (${\mathrm{C}}_{60}$). Using a scanning tunneling microscope tip, the electrical current $I$ flowing as a function of tip displacement $s$ towards the molecule is investigated [ $I\left(s\right)$ characteristics]. The tunneling current increases approximately exponentially with tip displacement in the tunnel regime, but this behavior changes significantly as contact is established. From the $I\left(s\right)$ data and calculations for ${\mathrm{C}}_{60}$ we determine an apparent electrical resistance of 54.80 M $\ensuremath{\Omega}$ for the junction at ``tip contact.'' In the Landauer formalism, this value is a measurement of the electronic transparence $2.35\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ of the molecule under the tip.