Cut chicken into thin strips. Wash red pepper, remove seeds, and cut into strips. Wash and pat dry the Thai basil leaves.
Heat a wok or deep pan over medium-high heat. Pour in the coconut milk and bring to a boil (3-5 minutes).
Stir the curry paste into the boiling coconut milk—it will be lumpy and take 2-3 minutes to fully combine. Panäng curry paste is quite spicy.
Add chicken strips, fish sauce, brown sugar, and lemongrass leaves. Reduce heat to medium and simmer for 8-10 minutes until the chicken reaches 74°C (165°F) internally.
Add red pepper strips and Thai basil leaves. Simmer for 2 more minutes. Remove and discard the lemongrass leaves.