Clean, wash, and pat dry the chicken pieces. Set them aside.
Heat oil in a wok or large saucepan over medium flame. Stir in the curry paste and cook for 2 to 3 minutes or till the oil starts separating from the paste.
Add chicken pieces. Stir-fry till chicken pieces turn pale white. Add 2 tablespoons of coconut milk if the curry paste sticks to the wok or burns.
Add sugar, fish sauce, vegetables, and salt. Combine and cook for 1 minute.
Add the remaining coconut milk along with kaffir lime leaves, water, red chillies, and stir to combine. Taste and season with salt accordingly.
Bring slowly to a boil, then reduce the heat to low and simmer, covered, for 6 – 8 minutes or until chicken and vegetables are cooked.
Before serving, add Thai basil and chopped cilantro.
Serve Thai Red Curry warm with jasmine rice.