Let Ω⊂ℂ n , n≥2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs–Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of ℂ n ∖Ω ¯ is ℂ n . It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in ℂ n for which the Hartogs phenomenon holds.