Context. The rich open cluster M67 is known to have a chemical composition close to solar, and an age around 4 Gyr. It thus offers the opportunity to check our understanding of the physics and the evolution of solar-type stars in a cluster environment. Aims. We present the first spectroscopic study at high resolution, R ≈ 50 000, of the potentially best solar twin, M67-1194, identified among solar-like stars in M67. Methods. G dwarfs in M67 (d ≈ 900 pc) are relatively faint (V ≈ 15), which makes detailed spectroscopic studies time-consuming. Based on a pre-selection of solar-twin candidates performed at medium resolution by Pasquini et al. (2008, A&A, 489, 677), we explore the chemical-abundance similarities and differences between M67-1194 and the Sun, using VLT/FLAMES-UVES. Working with a solar twin in the framework of a differential analysis, we minimize systematic model errors in the abundance analysis compared to previous studies which utilized more evolved stars to determine the metallicity of M67. The differential approach yields precise and accurate chemical abundances for M67, which enhances the possibility to use this object in studies of the potential peculiarity, or normality, of the Sun. Results. We find M67-1194 to have stellar parameters indistinguishable from the solar values, with the exception of the overall metallicity which is slightly super-solar ([Fe/H] = 0.023 ± 0.015). An age determination based on evolutionary tracks yields 4.2 ± 1.6 Gyr. Most surprisingly, we find the chemical abundance pattern to closely resemble the solar one, in contrast to most known solar twins in the solar neighbourhood. Conclusions. We confirm the solar-twin nature of M67-1194, the first solar twin known to belong to a stellar association. This fact allows us to put some constraints on the physical reasons for the seemingly systematic departure of M67-1194 and the Sun from most known solar twins regarding chemical composition. We find that radiative dust cleansing by nearby luminous stars may be the explanation for the peculiar composition of both the Sun and M67-1194, but alternative explanations are also possible. The chemical similarity between the Sun and M67-1194 also suggests that the Sun once formed in a cluster like M67.