Boil the chicken breast, let it cool, then shred it along the grain.
Julienne the carrot and place it in a bowl.
Mix olive oil, lemon juice, salt, and pepper with the carrot to make carrot râpée.
Cut the bread in half and layer the shredded chicken breast and carrot râpée on the bread.
Finish the sandwich by adding Greek yogurt or mustard sauce to taste.