Heat the olive oil in a large skillet over medium heat.
Season the chicken breasts with oregano, salt, and black pepper on both sides.
Place the chicken in the skillet and cook for about 6-7 minutes on each side, or until golden brown and cooked through (internal temperature of 165°F / 75°C).
Once the chicken is cooked, add the minced garlic to the skillet and sauté for about 1 minute until fragrant.
Add the halved cherry tomatoes to the skillet, cooking them down for about 3-4 minutes until they start to soften.
Reduce the heat to low and sprinkle the mozzarella balls evenly over the chicken and tomatoes. Cover the skillet with a lid and let it sit for 3-5 minutes until the cheese melts.
Remove the skillet from heat and toss in the torn basil leaves. Drizzle with balsamic glaze just before serving.