The goal of this paper is to study the smallest brightening events observed in the EUV quiet Sun. We use commissioning data taken by the EUI instrument onboard the recently launched Solar Orbiter mission. On 2020 May 30, EUI was situated at 0.556AU from the Sun. Its HRIEUV telescope 17.4nm passband reached an exceptionally high two-pixel spatial resolution of 400km. The size and duration of small-scale structures is determined in the HRIEUV data, while their height is estimated from triangulation with the simultaneous SDO/AIA data. This is the first stereoscopy of small scale brightenings at high resolution. We observed small localised brightenings (campfires) in a quiet Sun region with lengthscales between 400km and 4000km and durations between 10 and 200s. The smallest and weakest of these HRIEUV brightenings have not been observed before. Simultaneous HRILYA observations do not show localised brightening events, but the locations of the HRIEUV events correspond clearly to the chromospheric network. Comparison with simultaneous AIA images shows that most events can also be identified in the 17.1nm, 19.3nm, 21.1nm, and 30.4nm passbands of AIA, although they appear weaker and blurred. DEM analysis indicates coronal temperatures peaking at log(T)~6.1-6.15. We determined the height of a few campfires, which is between 1000 and 5000km above the photosphere. We conclude that campfires are mostly coronal in nature and are rooted in the magnetic flux concentrations of the chromospheric network. We interpret these events as a new extension to the flare/microflare/nanoflare family. Given their low height, the EUI campfires could be a new element of the fine structure of the transition region/low corona: apexes of small-scale loops that are internally heated to coronal temperatures.
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