Growth of two-dimensional metals has eluded materials scientists since the discovery of the atomically thin graphene and other covalently bound 2D materials. Here, we report a two-atom-thick hexagonal copper-gold alloy, grown through thermal evaporation on freestanding graphene and hexagonal boron nitride. The structures are imaged at atomic resolution with scanning transmission electron microscopy and further characterized with spectroscopic techniques. Electron irradiation in the microscope provides sufficient energy for a phase transformation of the 2D structure--atoms are released from their lattice sites with the gold atoms eventually forming face-centered cubic nanoclusters on top of 2D regions during observation. The presence of copper in the alloy enhances sticking of gold to the substrate, which has clear implications for creating atomically thin electrodes for applications utilizing 2D materials. Its practically infinite surface-to-bulk ratio also makes the 2D CuAu particularly interesting for catalysis applications.