Heat olive oil in a large saucepan over medium heat. Add onion and 1/2 tsp of salt and cook, stirring occasionally, until onion is very soft, about 10 minutes. Stir in turmeric and cook a minute, then add chicken, broth, water, parsley, and another 1/2 tsp of salt. Bring to a boil then cover and simmer until chicken is cooked through, about 15 minutes. Remove chicken from the soup using a slotted spoon and transfer to a cutting board.