Place first 10 ingredients in a food processor; process until minced, scraping sides of bowl occasionally.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add ginger mixture; sauté 2 minutes. Add chicken; cook 2 minutes on each side. Add broth, coconut milk, and sugar, scraping pan to loosen browned bits; bring mixture to a boil. Cover, reduce heat, and simmer 45 minutes or until chicken is done.
Remove pan from heat. Remove chicken from pan, reserving liquid in pan; cool chicken slightly. Remove the meat from bones, and discard bones. Place pan over medium heat. Stir in chicken and lime juice; cook for 2 minutes or until thoroughly heated. Serve with lime wedges, if desired.