Cut chicken into thin strips, about one inch long by once forth inch wide and set aside.

In a saucepan or skillet over medium-low heat, stir coconut milk with curry paste, fish sauce and brown sugar until mixture reaches a simmer. Add chicken and return to simmer, stirring occasionally over medium-low heat until flavors have mellowed and chicken is cooked, about 15 minutes. Top each serving with shredded fresh basil. Pass sliced chile peppers separately, so diners may adjust heat to their own tastes. Serve with steamed jasmine rice.