In a Dutch oven or similar large, deep, sturdy pot, heat the coconut oil over medium heat. Add the yellow onion and sauté until it is softened and turning translucent, about 5 minutes.
Add the red curry paste and stir very quickly to coat the onion.
Add the coconut milk and basil and bring to a boil. Continue to boil, stirring periodically, until somewhat thickened, about 8 minutes.
Add the carrot and bell peppers. Boil and stir for 5 minutes more.
Reduce the heat to medium-low and add the chicken, bamboo shoots, peanut butter, fish sauce, Worcestershire sauce, and coconut sugar. Simmer, stirring often, until chicken is cooked through, about 4 to 6 minutes.
Remove from the heat. Stir in the lime zest and juice. Serve hot with rice and a sprinkle of chopped peanuts and basil.