In a large soup pot, heat olive oil over medium heat. Add onions and sauté for 3 to 5 minutes, until softened. Add celery, carrots and garlic and continue cooking for another 3 to 4 minutes.
Stir in turmeric, ginger, pepper and salt, then add chicken breasts and broth. Bring to a boil, then reduce heat to low; cover and simmer for about 15 minutes, until chicken is cooked through.
Remove chicken from pot and shred with two forks. Return to pot and add coconut milk, kale and lemon juice. Continue cooking for another 3 to 4 minutes, until kale is wilted.
