Preheat oven to 400 degrees with racks in upper and lower thirds. Cut four 12-by-17-inch pieces of parchment. Fold each in half crosswise to make a crease, then unfold and lay flat. Toss together bok choy leaves, tomatoes, shallot, 1 teaspoon thyme leaves, and oil in a large bowl. Season with salt and pepper.
Season chicken with salt and pepper. Dividing evenly, place bok choy mixture on one side of crease on each piece of parchment, then top with chicken and 2 thyme sprigs. Drizzle each with 1 tablespoon wine. Fold parchment over, then make small overlapping pleats to seal and create half-moon-shaped packets.
Bake on 2 rimmed baking sheets until chicken is cooked through, 22 minutes. Transfer to plates; serve immediately, carefully cutting packets open with kitchen shears.