Heat oil in large skillet over medium-high heat. Add chicken; cook, turning occasionally, until browned on all sides, about 5 minutes per side. Drain fat from skillet. Leave chicken in skillet; season chicken with salt and pepper.
Add onion and water to skillet; cook, covered, over medium-low heat for 20 minutes, stirring occasionally.
Stir in chili sauce and oregano; cook, uncovered, over low heat for 5 to 10 minutes or until chicken is no longer pink near bone, basting frequently.
Skim excess fat from sauce. Serve sauce over chicken. Sprinkle with Parmesan cheese.
