Heat oil over medium-high heat in a large rimmed skillet. Cook, stirring frequently, until onion is translucent, about 5 minutes.
Add rice, chilies, and seasonings to the pan. Cook for about a 1 minute more, then pour in broth and bring to a simmer. Simmer rice for about 10 minutes.
Add chicken to the pan and cook until rice is tender and chicken heated, about 3-5 minutes.
Next, stir in the cheese, and about ¾ of the chopped cilantro. Stir to allow cheese melt. Garnish with a sour cream, olives, and additional chopped cilantro.