Prep the vegetables: Thinly slice carrot, bamboo shoots, and yard long beans. Cut red chili and tear kaffir lime leaves.
Fry the curry paste: Heat oil in a pot over medium-high heat and fry green curry paste until fragrant.
Add the chicken: Add chicken pieces and stir until evenly coated with the paste.
Simmer with coconut milk: Pour in coconut milk and water. Add fish sauce and palm sugar. Simmer until chicken is cooked through.
Add the vegetables: Stir in carrot, bamboo shoots, yard long beans, chili, and kaffir lime leaves. Cook until vegetables are tender.
Prepare the noodles: Cook rice noodles according to package directions, then drain.
Serve: Place noodles in serving bowls, ladle over the curry soup, and garnish with fresh herbs if desired. Serve hot.