We demonstrate chalcogenide optical fiber couplers with a power-dependent coupling coefficient. The couplers are designed and fabricated using an As2Se3 fiber and characterized at a wavelength of 1938 nm, leading to a critical power of 126 W, the lowest ever reported for any optical fiber coupler. These nonlinear couplers enable all-optical switching and will be useful for passive mode-locking over a wide wavelength range from the telecommunication band to the mid-infrared.