Set your oven to 400 degrees Fahrenheit (200 degrees Celsius) to preheat.
In a medium bowl, combine balsamic vinegar, olive oil, honey, garlic, oregano, salt, and pepper and whisk until smooth.
Add the chicken breasts and halved potatoes to a large resealable bag or bowl and pour the marinade over them; seal and refrigerate for a minimum of 30 minutes.
Arrange the marinated chicken and potatoes evenly on a sheet pan, ensuring they are spread out in one layer.
Place the sheet pan in the oven and roast for 25 to 30 minutes, or until the chicken is cooked through and the potatoes are fork tender.
Before serving, sprinkle with fresh parsley to garnish and add a burst of color and fresh flavor.