Heat oil in large skillet over medium-high heat until hot. Add chicken pieces and onion; cook and stir 4 to 6 minutes or until chicken is no longer pink.
Add rice, broth, tomato and chiles; mix well. Bring to a boil. Reduce heat to low; cover and simmer 20 minutes.
Remove skillet from heat. Stir in cheese and oregano. Top with spoonfuls of sour cream. Cover; let stand 3 minutes or until thoroughly heated.