Combine cooked rice, chicken, spices, black beans, cilantro, and lime juice in a medium-sized bowl.
Heat a large griddle or non-stick pan to medium-high heat.
Sprinkle a small amount of shredded cheese on a tortilla. Top with about half a cup of rice, bean, and chicken mixture. Top with green peppers, olives, and a dollap or two of sour cream.
Fold in the ends and roll up the sides.
Place on the hot griddle and let it grill for about 4-5 minutes or until the bottom of the burrito is slightly browned and crispy. Flip over and grill 4-5 minutes on the other side.
Once browned and crunchy on each side, serve with salsa.