Dice the onion, mince the garlic, and grate the ginger. Add the onion, garlic, and ginger to a large soup pot with the olive oil and sauté over medium heat until the onions are soft and translucent.
While the onion, garlic, and ginger are sautéing, peel and chop the carrots, and chop the celery.
Once the onions are soft, add the turmeric, cumin, and red pepper flakes. Sauté for about minute more to toast the spices. Add the carrots and celery and sauté for a few minutes more, or just until they begin to soften.
Add the chicken breast to the pot along with the chicken broth. Place a lid on the pot, turn the heat up to medium-high, and bring the broth to a boil. Once boiling, turn the heat down to medium-low, and let the broth simmer for 30 minutes.
Once the chicken and vegetables have simmered in the broth for 30 minutes, remove the chicken breast and shred it with two forks. Return the shredded meat to the soup and add the coconut milk. Stir to combine and heat through over medium-low heat. Taste the soup and add salt to taste (I added ½ tsp).
To serve, ladle about 1 ⅓ cups soup into a bowl and top with ½ cup cooked rice, a few fresh cilantro leaves, and a wedge of lime.