Preheat oven to 475°F. Mix cherry tomatoes, oil, garlic, and crushed red pepper on rimmed baking sheet. Sprinkle with salt and pepper. Bake until tomatoes are soft and beginning to brown in spots, stirring occasionally, about 20 minutes. Transfer tomato mixture, including any juices, from sheet to large skillet. Add chicken to skillet and simmer until heated through, about 5 minutes.
Meanwhile, cook pasta in large pot of boiling salted water until just tender but still firm to bite, stirring occasionally. Ladle out 1/4 cup pasta cooking water and reserve. Drain pasta; return to pot.
Add tomato mixture, arugula, and reserved 1/4 cup pasta cooking water to pasta; toss over medium heat just until arugula begins to wilt, about 30 seconds. Season to taste with salt and pepper. Transfer pasta to bowl. Sprinkle with feta cheese and serve.
Per serving: calories, 478; total fat, 15 g; saturated fat, 5 g; cholesterol, 71 mg; fiber, 5 g Nutritional analysis provided by Bon Appétit