In small saucepan bring pomegranate juice to boiling; boil gently, uncovered, 5 to 8 minutes or until reduced to 1/4 cup. Remove from heat; set aside. Meanwhile, in a 12-inch skillet cook chicken in 1 tablespoon hot olive oil over medium-high heat for 6 to 8 minutes or until chicken is no longer pink, turning occasionally. Remove chicken from skillet. Keep warm.
Add onion, remaining oil, dried oregano (if using), pepper, and salt to skillet; cook for 3 to 5 minutes or until onion is just tender, stirring occasionally. Stir in reduced pomegranate juice and the vinegar; bring to boiling. Boil 1 minute. Remove from heat and stir in fresh oregano (if using). Gradually add spinach, tossing just until spinach is wilted and combined.
Place spinach mixture in a large shallow dish. Top with chicken, pomegranate seeds, and nuts. Serve immediately.