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Ultrasmooth single-crystalline metallic thin films provide several key advantages for the fabrication of well-defined and high-resolution plasmonic nanostructures, particularly complex integrated nanocircuits. For this purpose, copper is generally regarded as a poor plasmonic material compared to gold and silver because of its notorious oxidation issues when subjected to air exposure. Here, we report on the use of large-area grain-boundary-free copper films grown epitaxially on sapphire substrates in combination with focused ion beam milling to pattern plasmonic nanostructures with superior quality. The copper surfaces prepared using a single-crystalline copper sputtering target exhibit a very low roughness without any grain boundaries for varying film thicknesses and a strong resistance to oxidation, overcoming the bottleneck in conventional copper film fabrication. Surface plasmon resonance measurements show that improved dielectric constants with higher conductivity and long-term stability can be achieved using the single-crystalline copper films. Plasmonic nanohole arrays patterned from these high-quality films are found to display a stronger field enhancement compared to those made from polycrystalline copper films, thus resulting in an enhanced extraordinary optical transmission performance. This study suggests that our fabrication method is ideally suited for applications in copper-based plasmonic and nanophotonic devices as well as integrated nanocircuits on a large scale.