In a small saucepan, add balsamic vinegar, brown sugar, and black pepper for the reduction. Heat over high heat, cooking until thickened, stirring occasionally. Keep over low heat until ready to serve.
In a large shallow bowl, stir together the olive oil, balsamic vinegar, garlic, oregano, basil, salt and pepper. Add in the chicken and allow to marinate for half an hour in the refrigerator. You can also marinate overnight.
When ready to cook, preheat grill. Once grill is hot, add chicken and grill for 5 to 6 minutes per side, until cooked through.
While the chicken is cooking, grill tomato slices and avocado halves for about 1 to 2 minutes per side. Remove avocado from peel and slice.
Remove chicken from heat and add to a baking sheet. Top each breast with one to two slices of grilled tomato. Top with one to two slices of grilled avocado. Top each with one slice of mozzarella.
Allow the heat to melt the cheese. If you need to, add baking sheet to the oven and broil on Low until cheese is melted.
Top with shredded basil and balsamic reduction. Serve immediately.