Heat oil in wok skillet, stir in green curry paste, about 2 minutes.
Stir in coconut milk, brown sugar and fish sauce and bring to a gentle boil on medium heat for about 8-10 minutes.
Add chicken pieces and red bell pepper strips, cover skillet and let simmer on medium low heat for about 30 minutes or until chicken is cooked.
Lower heat and stir in Thai basil leaves, Kaffir lime leaves and lime juice, and let simmer for 3-5 minutes.
Serve in bowls poured over jasmine rice or rice of your choice.