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We report continuous-wave (CW) operation of a 4.4-THz quantum-cascade laser grown in the GaAs-AlGaAs materials system by molecular beam epitaxy. The device operates at 4 K with a threshold current of 160 mA, and an output power of ∼25 μW. In pulsed mode, the maximum operating temperature is 52 K, with a threshold current of 108 mA at 4 K. CW lasing was achieved by using a small cavity ridge area (60×600 μm), and by coating one of the laser facets. These two features allowed for a substantial decrease of the threshold current and therefore reduced detrimental heating effects. The role played by the lateral resistance of the 800-nm GaAs layer underneath the active region was also investigated. Experimental data is presented showing that the temperature of the active region, which eventually hinders CW lasing, can be substantially influenced by the value of this lateral resistance.