Despite numerous experimental studies since 1824, the binary copper(I) fluoride remains unknown. A crystal structure prediction has been carried out for CuF using the USPEX evolutionary algorithm and a dispersion‐corrected hybrid density functional method. In total about 5000 hypothetical structures were investigated. The energetics of the predicted structures were also counter‐checked with local second‐order Møller–Plesset perturbation theory. Herein 39 new hypothetical copper(I) fluoride structures are reported that are lower in energy compared to the previously predicted cinnabar‐type structure. Cuprophilic Cu−Cu interactions are present in all the low‐energy structures, leading to ordered Cu substructures such as helical or zig‐zag‐type Cu−Cu motifs. The lowest‐energy structure adopts a trigonal crystal structure with space group P3121. From an electronic point of view, the predicted CuF modification is a semiconductor with an indirect band gap of 2.3 eV.