In a mortar or small bowl, mix the red curry paste, chopped green chilies, and sliced lemongrass until well combined.
Heat the oil in a heavy-bottomed pan over medium heat. Add the curry paste mixture and cook for about 1 minute until fragrant. Add the chicken pieces and stir to coat them with the paste.
Pour in the chicken broth along with the fish sauce and sugar. Bring the mixture to a simmer and cook for 15 minutes until the chicken is tender. Then add the baby corn, green beans, and eggplant.