Heat the oil in a wok over low heat. Add the green curry paste and stir until fragrant.
Add chicken and 1/2 cup of coconut milk and simmer, stirring constantly, until the chicken is cooked through. Add the remaining coconut milk and bring to a boil. Add the eggplant and baby corn and simmer until the eggplant is soft.
Season to taste with fish sauce and sugar. Stir in the basil, kaffir lime leaves and chilli (the lime leaves are for flavour, not to be eaten). Serve with rice.