Set your oven to preheat at 400°F (200°C).
Combine balsamic vinegar, olive oil, honey, minced garlic, dried oregano, salt, and pepper in a mixing bowl and whisk until smooth.
Put the chicken breasts and halved baby potatoes into a large zip-top bag or bowl, pour the marinade over them, close the bag or cover the bowl, and let sit for at least 30 minutes.
Arrange the marinated chicken and potatoes evenly onto a sheet pan in a single layer.
Cook in the oven for 25 to 30 minutes until the chicken is fully cooked and the potatoes are soft.
Before serving, sprinkle fresh parsley over the top for a bright finishing touch.