Heat oil in heavy large pot over medium-high heat. Sprinkle chicken with salt and pepper. Add chicken to pot and sauté until light golden but not cooked through, about 1 minute. Transfer chicken to bowl.
Add onion to pot and sauté until golden, about 4 minutes. Add garlic and stir 1 minute. Add curry powder, cumin and cinnamon stick and stir 30 seconds. Add sweet potatoes, parsnips, turnips, rutabaga, broth and currants. Cover and simmer until vegetables are tender, about 20 minutes. Add tomatoes and chicken with any accumulated juices to pot. Simmer until chicken is cooked through and flavors blend, about 5 minutes longer. Sprinkle with cilantro and serve.