Cut the chicken into bite-size pieces. Chop the onion and bell peppers into roughly 1-inch pieces, mince the garlic, and crush the kaffir lime leaves to release their oils.
Heat the coconut oil in a 14-inch skillet or wok over medium-high heat until melted and shimmering.
Add the chopped onion and sauté for 1 minute, then add the chopped peppers and minced garlic and sauté 2–3 minutes until slightly softened.
Push the vegetables to the sides of the skillet. Add the Panang red curry paste and peanut butter to the center and sauté 2–3 minutes, stirring, until fragrant and the paste darkens slightly.
Add the crushed kaffir lime leaves, coconut milk, and fish sauce to the pan and stir to combine into a smooth sauce.
Stir in the chopped chicken, bring the mixture to a boil, then reduce heat to a simmer. Cook 10–15 minutes, stirring occasionally, until the chicken is cooked through and the sauce thickens.
Remove from heat and stir in the Thai basil leaves. Serve immediately with rice, quinoa, or noodles.