We present the results of an optical light-curve 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 light-curve ranges ($1 mag) and long rotation periods (<2 rotations day À1 ) consistent with a contact binary nature. The optical light curves of both asteroids are well matched by Roche binary equilibrium models. Using these binary models, we find low densities of $600 and 800 kg m À3 , 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.