Set your oven to preheat at 400 degrees Fahrenheit or 200 degrees Celsius.
Combine the balsamic vinegar, olive oil, honey, minced garlic, oregano, salt, and pepper in a mixing bowl and whisk until fully blended.
Add the chicken breasts and halved baby potatoes to a large sealable bag or bowl and pour the marinade over them; seal the bag or cover and let everything marinate for at least half an hour.
Arrange the marinated chicken and potatoes evenly on a sheet pan without overlapping.
Roast the chicken and potatoes in the oven for between 25 and 30 minutes until the chicken is cooked through and the potatoes are soft.
Sprinkle fresh parsley on top before serving to add a burst of color and freshness.