Heat oven to 400°F. Toss broccoli with garlic, 1 tablespoon oil and ¼ teaspoon each salt and pepper. Divide among four 12-inch squares of parchment paper. Season chicken with ¼ teaspoon each salt and pepper and place on top of broccoli. Cover with second piece of parchment and fold up edges to seal. Place packets on 2 rimmed baking sheets and roast 15 minutes.
Meanwhile, from lemon, finely grate zest and squeeze 2 tablespoons juice. In medium bowl, combine onion, lemon juice, remaining tablespoon oil and ¼ teaspoon each salt and pepper. Let sit 4 minutes, then toss with tomatoes.
When chicken is done, transfer to serving plates. Cut open packets; top with tomato vinaigrette and sprinkle with lemon zest.
