We report the first demonstration of an all solid-state heterodyne receiver that can be used for high-resolution spectroscopy above 2?THz suitable for space-based observatories. The receiver uses a NbN superconducting hot-electron bolometer as mixer and a quantum cascade laser operating at 2.8?THz as local oscillator. We measure a double sideband receiver noise temperature of 1400?K at 2.8?THz and 4.2?K, and find that the free-running QCL has sufficient power stability for a practical receiver, demonstrating an unprecedented combination of sensitivity and stability.