Set your oven to 400°F (200°C) to begin heating.
In a mixing bowl, combine balsamic vinegar, olive oil, honey, garlic, oregano, salt, and pepper and whisk thoroughly.
Add the chicken breasts and halved baby potatoes to a large bowl or resealable bag and pour the marinade over them; seal and let them marinate for at least 30 minutes.
Arrange the chicken and potatoes evenly on a sheet pan in one layer to prepare for baking.
Place the sheet pan in the oven and cook for 25 to 30 minutes until the chicken is fully cooked and potatoes are soft.
Sprinkle fresh parsley on top just before serving to add a fresh touch.