Combine first 5 ingredients (thyme through chiles) in a food processor; process until finely chopped. Remove 1/4 cup of the chile mixture and set aside. Add lime juice to food processor; process until smooth.
Arrange chicken in a large shallow dish. Spread lime juice mixture over chicken. Cover and marinate in refrigerator 4 hours.
Place chicken on a broiler pan coated with cooking spray; broil 15 minutes on each side or until done.
While chicken broils, prepare rice mixture. Heat oil in a large saucepan over medium-high heat. Add reserved 1/4 cup chile mixture; saute 2 minutes. Stir in rice. Add broth; bring to a boil. Cover, reduce heat, and simmer 5 minutes. Stir in sweet potato; cook 10 minutes. Stir in beans; cook 3 minutes or until liquid is absorbed. Remove from heat; let stand, covered, 5 minutes. Drizzle with Pickapeppa sauce, if desired. Garnish with lime wedges.
Note: Made from cane vinegar aged in oak barrels, Pickapeppa sauce is a sweet and sour, mild hot-pepper sauce from Jamaica.