In a small bowl, combine cumin, chili powder, garlic powder, and salt. Toss with chicken strips to coat evenly.
Heat olive oil in a large skillet over medium-high heat. Cook chicken until internal temperature reaches 165 degrees Fahrenheit. This usually takes 6 to 8 minutes.
In a separate small saucepan, combine cubed white American cheese and milk over low heat.
Whisk the cheese mixture continuously until completely melted and smooth. Avoid letting the sauce boil.
Stir the diced green chilies into the cheese sauce. Remove the pan from the heat immediately.
Divide the cooked Mexican rice among four plates evenly.
Place a portion of the seasoned chicken on top of the rice.
Generously ladle the warm cheese sauce over the chicken and rice before serving.