Heat the oil in a sauce pan over medium heat and add Thai green curry paste, stir regularly to prevent the paste from burning. When the curry paste is dissolved and the color changes, go to the next step.
Add coconut cream, chicken and cook until fragrant. Bring to a low boil then add eggplant, kaffir lime leaves, fish sauce, sugar and then coconut milk.
Simmer until chicken is cooked then turn remove from stove and transfer into serving bowl. Garnish with sweet basil leaves.