In 12-inch skillet, heat 1 tablespoon of the oil over medium-high heat. Cook chicken in oil in batches 5 minutes, stirring frequently, until no longer pink in center. Remove from skillet; cover to keep warm.
In same skillet, heat remaining 2 tablespoons oil over medium-high heat. Cook onion in oil 3 to 5 minutes, stirring occasionally, until softened. Add mushrooms; cook 5 minutes or until light golden brown. Add broth, scraping bottom of skillet to loosen browned particles.
Stir in rice mix with seasoning packet until blended. Heat to boiling; reduce heat to low. Cover; simmer 25 minutes or until rice is tender. Stir in chicken. Cook just until chicken is thoroughly heated. Remove from heat; stir in sour cream, salt and pepper. Sprinkle with parsley.