Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Wash and dice the Yukon Gold potato into 1/2-inch cubes and slice the zucchini into half-moons.
Place the potatoes, zucchini, and cherry tomatoes on the baking sheet and toss with 0.5 tbsp of olive oil, dried oregano, and half of the salt and pepper.
Roast the vegetables in the oven for 15 minutes.
While the vegetables are roasting, season the chicken breast with the remaining salt and pepper.
Heat the remaining 0.25 tbsp of olive oil in a skillet over medium-high heat and sear the chicken for 3 minutes on each side until a golden crust forms.
Add the minced garlic to the skillet for 30 seconds, then pour in the balsamic vinegar, allowing it to bubble and reduce slightly.
Transfer the chicken and the balsamic pan drippings to the baking sheet with the vegetables.
Return the sheet to the oven for another 10 minutes, or until the chicken reaches an internal temperature of 165°F.
Garnish with chopped fresh parsley and serve immediately.