Cook the barley according to the package directions.
Meanwhile, heat the oil in a large pot or Dutch oven. Add the carrots, celery, onions, parsnips, 1 teaspoon salt, and 1/2 teaspoon pepper. Cook, covered, stirring occasionally, until the vegetables begin to soften, 20 to 25 minutes.
Add the tomatoes (and their juices) and 8 cups water. Simmer, stirring occasionally, until the soup has slightly thickened and the vegetables are tender, 45 to 60 minutes.
Add the kale and simmer, stirring occasionally, until it is tender, 5 to 6 minutes. Stir in the chickpeas and cooked barley and cook until heated through, about 3 minutes.