Coat a large baking dish (I used my cast iron braising pan) with 1 tablespoon of the olive oil.
In a large bowl, combine the rest of the olive oil, lemon juice, garlic, salt, and pepper.
Add the broccoli to the to the oil mixture. Toss and remove them with a slotted spoon and place them on the bottom of the pan. Repeat using the potato chunks. Place the potatoes around the inner edge of the pan, on top of the broccoli.
Place the chicken breasts, one at a time in the oil mixture and coat thoroughly on both sides. Place in the center of the pan.
Pour the remainder of the oil mixture over the top of the chicken in the pan, and roast for 50-60 minutes.
When the chicken is done, remove it, and return the pan to the oven to cook for a few more minutes if needed until the vegetables are fork tender.