Combine first 5 ingredients, and rub oregano mixture over chicken. Cover and marinate in refrigerator 30 minutes.
Heat oil in a large nonstick skillet over medium-high heat; add chicken thighs, and cook 5 minutes on each side or until browned. Remove chicken from skillet; keep warm. Add cider to skillet, scraping pan to loosen browned bits.
Bring to a boil; cook until reduced to 1 cup (about 3 minutes). Remove 1/2 cup reduced cider from skillet; set aside.
Add cabbage and remaining ingredients to skillet; bring to a boil. Cover, reduce heat to medium, and cook 5 minutes or until cabbage wilts.
Return chicken thighs to skillet, nestling them into cabbage mixture; add reserved 1/2 cup reduced cider. Cover and cook over medium-low heat 30 minutes or until chicken is done.