Place the oven rack into the middle position and preheat the oven to 400F (205C). You can line the baking sheet with parchment paper for easy cleanup.
Drizzle a little olive oil (about a tablespoon) on the baking sheet. Place the cherry tomatoes, chopped garlic, and fresh thyme on the sheet.
Trim the chicken quarters of excess fat and pat them dry with a paper towel. Generously season them with salt and pepper on both sides, and place them in the baking tray, on top and around the tomatoes, skin-side up.
Drizzle the remaining olive oil over the chicken quarters.
Bake:
Bake for 40 to 45 minutes in the preheated oven or until the internal temperature has reached 175F (80 C).
Halfway through cooking, I like to baste the chicken quarters with some of the juices in the pan. If you don't have a baster, remove the pan from the oven, use kitchen tongs to flip the quarters over a couple of times to coat them with the drippings, and return the pan to the oven with the chicken skin-side-up.
Remove the baking sheet from the oven and let it rest for 5 minutes while you gather your sides.
Serve:
Plate the leg quarters and spoon the roasted tomatoes and garlic pieces from the pan over the chicken.