We present the results of an optical lightcurve survey of 114 Jovian Trojan asteroids conducted to determine the fraction of contact binaries. Sparse-sampling was used to assess the photometric range of the asteroids and those showing the largest ranges were targeted for detailed follow-up observations. This survey led to the discovery of two Trojan asteroids, (17365) and (29314) displaying large lightcurve ranges (~1 magnitude) and long rotation periods (< 2 rotations per day consistent with a contact binary nature. The optical lightcurves of both asteroids are well matched by Roche binary equilibrium models. Using these binary models, we find low densities of ~600 kg/m^3 and 800 kg/m^3, suggestive of porous interiors. The fraction of contact binaries is estimated to be between 6% and 10%, comparable to the fraction in the Kuiper Belt. The total binary fraction in the Trojan clouds (including both wide and close pairs) must be higher.