Combine first 3 ingredients; sprinkle over both sides of chicken.
Heat oil in a large nonstick skillet over medium-high heat. Add chicken; cook 5 minutes. Turn chicken, and add salsa to pan. Cover, reduce heat, and simmer 7 minutes or until chicken is done.
Transfer chicken onto individual serving plates. Stir avocado and cilantro into salsa in pan; cook just until thoroughly heated. Spoon salsa mixture over chicken.