In a large skillet, heat the olive oil over medium heat. Add the chicken pieces, salt, and pepper, cooking until the chicken is browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and garlic. Sauté for about 2-3 minutes until the onion is translucent.
Stir in the uncooked rice and cook for an additional 1-2 minutes, allowing the rice to toast slightly.
Pour in the chicken broth and salsa verde, stirring to combine. Bring the mixture to a boil.
Reduce the heat to low, cover the skillet, and simmer for about 15 minutes, or until the rice is tender and has absorbed most of the liquid.
Add the corn, black beans, and cooked chicken back into the skillet. Stir to combine and heat through for another 2-3 minutes.
Remove from heat and sprinkle the shredded cheese on top. Cover the skillet for a few minutes until the cheese is melted.
Garnish with fresh cilantro and serve with lime wedges on the side.