While the grill is heating up, trim the chicken breasts and cut them in half lengthwise. Season both sides of each piece with salt and pepper.
Drizzle olive oil over the tomatoes and onions and seasoned with salt and pepper. You can use a mixing bowl for the onions so you can stir them, but the tomatoes will fall off the vine if you try to mix them in bowl.
Use a slotted vegetable grill tray to cook the tomatoes and onions on the grill while the chicken is cooking.
When serving, drizzle some balsamic vinegar glaze over the tomatoes and onions.