Season the chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 4 minutes per side or until they are browned. Remove the chicken from the skillet and set aside.
In the same skillet, add a bit more olive oil if needed. Add the sliced onions and cook until they become soft and translucent (about 5-6 mins.)
Add minced garlic, dried thyme, and dried rosemary to the onions. Sauté for an additional 30-60 seconds until the garlic becomes fragrant.
Pour in the balsamic vinegar and chicken broth, stirring to combine. Add sugar-free maple syrup or a low-carb sweetener if using. Bring the mixture to a boil and reduce to a simmer.
Return the cooked chicken breasts to the skillet, spooning some of the balsamic mixture over them. Add the halved cherry tomatoes and cover.
Cover with a lid and let chicken simmer for 20-30 minutes or cook through.
Drop in the mozzarella cheese balls, cover for about 2-3 minutes or until the cheese balls have become melted.
Garnish with fresh basil or parsley before serving.