In a large pot, heat the coconut milk over medium heat.
Add the green curry paste and stir until well combined.
Add the sliced chicken and cook until browned.
Incorporate the diced eggplant and bamboo shoots into the mixture.
Stir in the bell peppers and cook for another 5 minutes.
Add fish sauce and sugar, mixing well.
Let the curry simmer for about 10 minutes.
Taste and adjust seasoning if needed.
Remove from heat and stir in fresh basil leaves.
Serve hot with lime wedges on the side.