Heat 2 teaspoons oil in a large saucepan over medium-high heat. Add onion, parsnips, carrot, apple, rosemary, salt and pepper and cook, stirring often, until the vegetables begin to soften, about 8 minutes. Add broth and water and bring to a simmer over high heat. Reduce heat to maintain a simmer and cook, stirring often, until the vegetables are very tender, about 10 minutes.
Transfer the soup to a blender; add vinegar, cover and pulse until it forms a chunky puree. (Use caution when pureeing hot liquids; see Tip.)
Clean the pot, return it to medium-high heat and add the remaining 1 teaspoon oil. Add chicken and cook, stirring occasionally, until lightly browned, 3 to 4 minutes. Pour the soup back into the pan. Cook, scraping up any browned bits from the bottom of the pan, until heated through, about 1 minute.