Heat the skillet over medium-high heat and add a tablespoon of oil until shimmering. Add the sliced chicken and cook, stirring occasionally, until it's browned and cooked through, about 5-7 minutes. Remove the chicken from the pan and set aside.
Add another tablespoon of oil to the same skillet. Toss in the sliced peppers and cook until they are blistered and lightly charred around the edges, about 5 minutes. Stir frequently to promote even charring and soften the peppers.
Sprinkle the chili powder, cumin, salt, and pepper over the peppers. Stir well to coat the vegetables in the spices, allowing the flavors to bloom and the peppers to become fragrant.
Return the cooked chicken to the skillet, mixing with the peppers. Let everything cook together for another 2-3 minutes to heat through and allow the flavors to meld. The mixture should be sizzling and vibrant in color.
Check for seasoning and adjust salt and spices if needed. Once the chicken is hot and the peppers are slightly charred in spots, remove the skillet from heat.
Serve the fajitas hot, with tortillas or on their own, enjoying the smoky, tender chicken and crisped peppers. The dish is best enjoyed immediately for maximum flavor and texture.