Molecular dynamics computer simulations have been employed with a Finnis-Sinclair form of interatomic potential to calculate the properties of point defects in Cu3Au and to establish the threshold displacement energy, E-d, for both C and Au primary knock-on atoms in this alloy. The most stable interstitial is the Cu-Cu[100] dumbbell centred on a Cu site in the {100} plane which contains only Cu atoms, and all configurations of a Au interstitial are unstable with respect to the formation of a Cu antisite defect plus a Cu-Cu[100] interstitial. The results are compared with those of Spaczer, Caro and Victoria, who used embedded-atom potentials and whose data for antisite defects are different from those found here. E-d for Au recoils has a lower value on average than that for Cu recoils, in contrast with the threshold energy of recoils of the oversized species Al in Ni3Al. For Curecoils, however, the E-d values are very similar to those found for Ni recoils in Ni3Al, particularly for orientations in which Cu-Cu interactions dominate. In a crystal at 0 K, a long replacement collision chain can be formed without generating stable Frenkel pairs. The results are discussed in terms of the structure and atomic interactions and compared with the experimental data.