Heat the olive oil in a large skillet over medium-high heat.
Add the chicken and cook until browned, 7 to 8 minutes.
Add onion and cook until softened, 4 to 5 more minutes.
Add beans, tomatoes and water; bring to a boil. Stir in quinoa & brown rice, cover and cook for 10 minutes.
Remove lid and cook 5 to 10 more minutes, or until most of liquid has been absorbed and the mixture is thick.
Sprinkle cheese over the top and place skillet under a preheated broiler until bubbly and cheese begins to brown, 5 to 8 minutes. (If the skillet isn’t ovenproof, transfer mixture to a 9-inch or 9 x 13-inch baking dish, top with cheese and broil.)
Serve immediately; garnish with sliced green onions if desired.
Notes: Green chilies or red pepper flakes can be added to taste for a spicier southwestern flavor, if desired.