In a medium bowl, whisk together balsamic vinegar, olive oil, and brown sugar until well combined. Add minced garlic and dried basil, seasoning with a pinch of salt. Set aside a portion of the marinade for later.

Place chicken thigh fillets in a shallow dish and pour marinade over, ensuring they're evenly coated. Cover and refrigerate for at least 30 minutes.

Heat a grill pan over medium-high heat. Add marinated chicken and cook for about 6-7 minutes on each side until golden brown and cooked through. Allow to rest before slicing.

In a large bowl, combine chopped romaine lettuce, sliced avocados, halved cherry tomatoes, and mozzarella balls. Mix gently.

Drizzle the reserved marinade over the salad and toss gently to combine, ensuring all ingredients are coated evenly.