In a 12-inch skillet, heat oil over medium heat. Add the 1 cup chopped onion; cook about 4 minutes or until tender. Add chicken and garlic; cook about 4 minutes more or until chicken is browned, turning once. Stir in broth, poultry seasoning, black pepper, and crushed red pepper. Bring mixture to boiling. Stir in uncooked rice. Reduce heat. Cover and cook about 10 minutes or until rice is almost tender. Stir in black-eyed peas and the 1 tablespoon thyme. Cover and cook about 10 minutes or until heated through and liquid is absorbed. If desired, garnish with additional finely chopped red onion and snipped thyme.