Heat the oil in a large saucepan Add the apple and the sweet potato and cook until apple is soft. Stir in the garlic, cumin, thyme and salt and continue cooking for 1 more minute.
Add the broth and the chicken and bring to a boil. Reduce heat and simmer until chicken is cooked through and sweet potatoes are tender. Remove the chicken breasts and shred with two forks. Add back to the pot and simmer until heated through before serving topped with the fresh parsley.