Wash the chicken fillets and pat them dry. Heat 1 tablespoon of oil in a saucepan. Fry the meat for about 15 minutes. Season with salt and pepper. Remove the fillets and keep them warm. In the meantime peel and slice the carrots.
Clean, wash and cut the peppers into strips. Clean, wash and cut the sugar snap peppers into pieces. Peel and finely chop garlic and ginger. Add 1 tablespoon of oil to the pot and heat. Fry vegetables, ginger and garlic in it.
Dust with curry. Wash and halve lemon grass and flatten it with a knife. Cut the meat into slices. Add stock, lemon grass and coconut milk to the vegetables, bring to the boil and simmer for 5 minutes.
Remove the lemon grass. Add slices of meat to the soup. Season soup with salt, pepper and lime juice. Arrange on plates. Cut lime into slices and garnish the soup with them.