Heat the oil in a large saucepan over medium high heat. Add the onion, carrot, and garlic and cook until softened.
Add the curry powder and cook for a minute. Add the broth and the tomatoes, and bring to a boil. Reduce to a simmer and add the chicken, coconut milk, lime juice, and cilantro. Simmer on low for 5 minutes.
Serve the soup hot, sprinkled with coconut flakes if desired.