Make the fajita seasoning: Combine the black pepper, salt, chili powder, cumin, garlic powder, paprika, coriander, oregano, and cayenne in a small dish and set aside.
For the fajitas: Preheat the oven to 425° and move the oven rack to the middle level. Spray a large sheet pan with cooking spray.
Spread the sliced vegetables in one layer on the sheet pan and drizzle with 2 tablespoons of olive oil. Sprinkle 2 tablespoons of fajita seasoning over the top of the vegetables. Toss to coat.
Place the chicken strips into a bowl and drizzle with the remaining 2 tablespoons of olive oil.
Add the remaining fajita seasoning to the chicken and toss with tongs or a rubber spatula until the chicken is completely coated.
Arrange chicken strips on top of vegetables in one layer. Ensure that no pieces of chicken are stuck together.
Bake for 15-20 minutes until the thickest piece of chicken registers 165F on a meat thermometer and is no longer pink inside.
Toss the chicken and veggies so that they are evenly coated in spices and juices.
Move the oven rack to the third position from the top and return the sheet pan to the oven.
Set the broiler to high heat and broil the chicken and vegetables until the chicken starts to get a little crisp on the edges and the veggies start to get a little char on them, 3-5 minutes.
Remove from oven and serve in a warm tortilla or on top of cooked rice.