Heat olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and sauté for about 3-4 minutes until soft.
Add minced garlic to the pot and cook for an additional minute, stirring frequently to avoid burning.
Add the diced chicken breast to the pot, followed by the dried oregano and basil. Season with salt and pepper. Cook the chicken for about 5-7 minutes until it's no longer pink.
Pour in the chicken broth and diced tomatoes (with their juice). Bring the mixture to a boil, then reduce the heat and let it simmer for about 10 minutes.
Stir in the gnocchi and cherry tomatoes, cooking for another 3-5 minutes until the gnocchi are tender and cooked through.
Remove the pot from heat and stir in the mozzarella balls and balsamic vinegar until the cheese is slightly melted.
Serve the soup hot, garnished with fresh basil leaves.
For extra creaminess, you can stir in a splash of heavy cream or some grated Parmesan cheese at the end.
Feel free to adjust the amount of chicken and vegetables based on your preferences.
This soup can be stored in the refrigerator for up to 3 days and reheats well on the stove.