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We have investigated the thermal stability of sputter-deposited Cu thin films with a high density of nanoscale growth twins by using high-vacuum annealing up to 800 C for 1 h. Average twin lamella thickness gradually increased from approximately 4 nm for as-deposited films to slightly less than 20 nm after annealing at 800 C⁠. The average columnar grain size, on the other hand, rapidly increased from approximately 50 to 500 nm. In spite of an order of magnitude increase in grain size, the annealed films retained a high hardness of 2.2 GPa, reduced from 3.5 GPa in the as-deposited state. The high hardness of the annealed films is interpreted in terms of the thermally stable nanotwinned structures. This study shows that nanostructures with a layered arrangement of low-angle coherent twin boundaries may exhibit better thermal stability than monolithic nanocrystals with high-angle grain boundaries.