In a small saucepan on the stovetop, or in a microwave oven, bring the tomatoes and broth just to a boil. Let stand about 15 minutes, until the tomatoes are softened. Remove the tomatoes and reserve any remaining broth.

Cut the tomatoes in half. Use a small sharp knife to cut as large a pocket as possible in each chicken breast, taking care not to cut all the way through. Divide the rehydrated tomatoes and the basil among the chicken, stuffing them into the pockets. Sprinkle the chicken lightly with salt and pepper.

In a shallow dish just large enough to hold the chicken, combine the reserved broth, vinegar, oil, garlic, and red pepper. Let stand 30 minutes at room temperature or up to 2 hours in the refrigerator. Drain and discard the marinade.

Prepare a medium-hot fire. Lightly oil the grill or coat with a non-stick vegetable spray. Grill the chicken, turning once with a spatula, 8 to 10 minutes, until the meat is white throughout. Serve warm or at room temperature, cut into crosswise sections and fanned out if desired. 249 cals, 5.8 g fat (21.7% cff) Low Fat Grilling: Fabulous Food from the Backyard Barbecue by Melanie Bernard.