Make the marinade
In a bowl, mix the olive oil, balsamic vinegar, 1 tablespoon greek seasoning, parsley, and garlic. Whisk to combine.
Add the chicken and half the dressing to a bag, seal and move to coat the chicken breasts. Set aside.
Cut the potatoes in half and add to a bag with the remainder of the dressing. Seal and move to coat the potatoes.
Marinade for 30 minutes or overnight is best.
Arrange the sheet pan dinner
Preheat oven to 425F. Line a rimmed baking sheet with foil (for easy cleanup) or you can spray with non-stick spray.
Arrange the chicken and potatoes on the baking sheet leaving out the excess marinade from the bags.
Halve the tomatoes lengthwise and place on baking sheet. Drizzle the tomatoes with olive oil and sprinkle with remaining Greek seasoning.
Bake until chicken is cooked through and registers 165°F in the thickest part, about 22–30 minutes.
Remove chicken to a plate and rest for 10 minutes. If veggies aren't cooked to your liking, you can bake them more while the chicken rests.
Slice chicken and serve with veggies. Sprinkle with feta cheese.
Serve this with basmati rice or warm pita bread.