Using the High Energy Spectroscopic System (H.E.S.S.) telescopes we have discovered a steady and extended very high-energy (VHE) γ-ray source towards the luminous blue variable candidate LBV 1806−20, massive stellar cluster Cl* 1806−20, and magnetar SGR 1806−20. The new VHE source, HESS J1808−204, was detected at a statistical significance of >6σ (post-trial) with a photon flux normalisation (2.9 ± 0.4stat ± 0.5sys) × 10−13 ph cm−2 s−1 TeV−1 at 1 TeV and a power-law photon index of 2.3 ± 0.2stat ± 0.3sys. The luminosity of this source (0.2 to 10 TeV; scaled to distance d = 8.7 kpc) is LVHE ~ 1.6 × 1034(d/8.7 kpc)2 erg s−1. The VHE γ-ray emission is extended and is well fit by a single Gaussian with statistical standard deviation of 0.095° ± 0.015°. This extension is similar to that of the synchrotron radio nebula G10.0−0.3, which is thought to be powered by LBV 1806−20. The VHE γ-ray luminosity could be provided by the stellar wind luminosity of LBV 1806−20 by itself and/or the massive star members of Cl* 1806−20. Alternatively, magnetic dissipation (e.g. via reconnection) from SGR 1806−20 can potentially account for the VHE luminosity. The origin and hadronic and/or leptonic nature of the accelerated particles responsible for HESS J1808−204 is not yet clear. If associated with SGR 1806−20, the potentially young age of the magnetar (650 yr) can be used to infer the transport limits of these particles to match the VHE source size. This discovery provides new interest in the potential for high-energy particle acceleration from magnetars, massive stars, and/or stellar clusters.Key words: gamma rays: general / stars: magnetars / stars: massive★ Wallenberg Academy Fellow.† Deceased.Read less <