Atomic structure of nanoscale particles of a Cu-Au alloy with a nominal composition Cu3Au and the phase transformation therein are studied by means of high-resolution electron microscopy and electron diffraction. The particles 8.8 nm in diameter on average prepared by simultaneous vacuum deposition of the constituent elements exhibit as a whole an fcc structure of an alloy with a composition of 26.4 at.% Au. The alloy particles are ordered into the L12-type superlattice structure when heat-treated at 563 K for 1 h. The superlattice reflections disappear upon heating up to 773 K. In a particle about 10 nm in size an antiphase domain boundary is observed. It thus appears that the nanoscale particles of the alloy undergo the order-disorder transition, as in the bulk. However, the critical temperature Tc for the order-disorder transition of the nanoscale particles is found to be by about 90 K lower than that of the bulk. The minimum size of the alloy particles in which lattice fringes whose spacing corresponds to the interplanar spacing of the {100}-type superlattice planes are observed is about 4 nm. These facts suggest that a certain critical size and size effects are present for atomic ordering in the Cu-Au alloy particles.