We find conditions for suppression of higher-order core modes in chalcogenide negative curvature fibers with an air core. An avoided crossing between the higher-order core modes and the fundamental modes in the tubes surrounding the core can be used to resonantly couple these modes, so that the higher-order core modes become lossy. In the parameter range of the avoided crossing, the higher-order core modes become hybrid modes that reside partly in the core and partly in the tubes. The loss ratio of the higher-order core modes to the fundamental core mode can be more than 50, while the leakage loss of the fundamental core mode is under 0.4 dB/m. We show that this loss ratio is almost unchanged when the core diameter changes and so will remain large in the presence of fluctuations that are due to the fiber drawing process.