A high-temperature furnace with an induction heater coil has been designed and constructed for in situ X-ray spectroscopic experiments under controlled atmospheric conditions and temperatures up to 3275 K. The multi-purpose chamber design allows working in backscattering and normal fluorescence mode for synchrotron X-ray absorption and emission spectroscopy. The use of the furnace is demonstrated in a study of the in situ formation of Cr oxide between 1823 K and 2023 K at logPO(2) values between -10.0 and -11.3 using X-ray absorption near-edge spectroscopy. The set-up is of particular interest for studying liquid metals, alloys and other electrically conductive materials under extreme conditions.