Bring 1/2 cup coconut milk to a boil in a heavy saucepan. Mix in the curry paste and cook until fragrant; about 5 minutes.
Add the chicken and cook until browned, about 5 minutes. Stir in the 2 cups coconut milk, fish sauce, sugar, vegetables, bamboo shoots and basil. Simmer until the chicken is cooked through; about 15 minutes.
Pour the lime juice over the dish and remove from heat. Serve warm.