Place chicken in 1-gallon zip bag. Add Lemon Vinaigrette, seal and marinate in refrigerator at least 30 minutes.
Cut each tomato into quarters, lengthwise. Place in medium bowl and toss gently with sugar, salt and olive oil. Spoon tomato mixture onto rimmed cookie sheet so that tomato pieces don't touch. Place in 375 degree oven and roast for 30 minutes.
Spoon tomatoes and all accumulated juices into small bowl. Add cheese, basil leaves and pepper, tossing gently. Let sit at room temperature while chicken cooks.
Remove chicken and discard marinade. Place chicken on same cookie sheet used to roast tomatoes. Roast at 350 degree for about 30 minutes, turning once.
To serve, place each chicken breast half on warmed dinner plate. Spoon 1/4 of tomato mixture over top.
Lemon Vinaigrette: In small bowl, whisk together olive oil, lemon juice, garlic, kosher salt and pepper.