Season the ingredients: Add the potatoes, onion, tomatoes, peppers, and olives to a large bowl, and the chicken to another bowl. Add half of each the garlic, oil, vinegar, salt, pepper, and paprika over the veggies, and the other half of these ingredients to the chicken. Toss everything well.
Roast: Dump the veggies into a large 9x13 baking dish. Arrange the chicken over the veggies. Roast for 1 hour, or until the chicken is cooked through and the potatoes are fork tender.
Serve - Sprinkle the fresh basil all over the chicken and veggies. Serve, and drizzle some of the pan juices over the chicken.
Leftovers will last you 4 days stored in an airtight container in the fridge. You can store the veggies and chicken separate if you prefer, but I just tossed everything together.
Reheat either in the microwave, or transfer the leftovers to a baking dish, cover with foil, and cook at 375F for about 10 minutes or until warmed through.
If you want to freeze your leftovers, they will last up 4 months stored in an airtight container or large freezer bag. Keep in mind that the veggies, after being cooked and frozen, will soften quite a bit.