Heat oil in a 5-quart Dutch oven over medium-high heat. Add chicken, cumin, paprika, chili powder and salt and cook for 4 minutes, stirring occasionally.
Add peppers and onion and cook for 4 minutes. Stir in garlic and rice for 1 minute.
Pour in broth and scrape the bottom clean. Bring to a simmer, cover tightly and reduce the heat to low.
Cook for 18 to 20 minutes until rice is tender and chicken reaches 165°F. Remove from the heat and rest covered for 5 minutes.
Fold in lime juice gently, scatter Monterey Jack over the surface and cover for 2 minutes to melt. Serve in 4 portions with the pepper strips distributed evenly.