Heat olive oil in a large frying pan (with sides at least 2 in. high) over medium-high heat. Sprinkle chicken with salt and pepper and cook, stirring often, until lightly browned but not cooked through, about 5 minutes. Remove chicken from pan and set aside.
Add onion, garlic, and jalapeños to pan, reduce heat to medium, and cook, stirring frequently, until onion is translucent, about 5 minutes. Add rice and cook, stirring, 1 minute more, then pour in broth and bring to a boil. Boil rice 5 minutes, then reduce heat to a simmer, cover pan, and cook 15 minutes.
Return chicken to pan and cook until rice is tender, liquid is absorbed, and chicken is cooked through, about 5 minutes.
Remove pan from heat and stir in chiles, cheese, and cilantro. Serve immediately.
Note: Nutritional analysis is per serving.