To make the Lemon Mustard Dressing, combine lemon juice, balsamic vinegar, mustard, salt, and pepper. Slowly whisk in oil. Set aside.
Preheat out door grill or stove top grill pan to very hot. Toss chicken with lemon juice, salt, pepper and olive oil to coat. Place on hot grill. Cook about 5 minutes. You want to get good ‘scoring’ or grill marks on the meat.
Preheat oven to 375 degrees. Mix the tomatoes olives, capers, squash. And red peppers together. Place in bottom of an ovenproof 12 x 9 inch pan. Lay chicken over vegetables. Pour on Lemon Mustard Dressing, reserving some of it. Cook for 15 min. in oven.
To serve, lift a chicken breast out of the pan along with the vegetables bedded underneath. Spoon over reserved Lemon Mustard Dressing. Serve with pasta or rice.