SEASON CHICKEN WITH ITALIAN SEASONING, GARLIC AND SALT. HEAT OIL IN A GRILL PAN OR SKILLET, AND SEAR CHICKEN BREASTS OVER MEDIUM-HIGH HEAT UNTIL BROWNED ON BOTH SIDES AND COOKED THROUGH (ABOUT 6 MINUTES EACH SIDE). REMOVE FROM PAN; SET ASIDE AND ALLOW TO REST.
COMBINE THE TOMATOES, RED ONION, BASIL, OLIVE OIL IN A BOWL. SEASON WITH SALT. TOP EACH CHICKEN BREAST WITH THE TOMATO MIXTURE AND PARMESAN CHEESE.
SERVE IMMEDIATELY WITH BALSAMIC GLAZE (OPTIONAL).
FOR THE BALSAMIC GLAZE:
(IF MAKING FROM SCRATCH, PREPARE WHILE CHICKEN IS COOKING.) COMBINE SUGAR (IF USING) AND VINEGAR IN A SMALL SAUCEPAN OVER HIGH HEAT AND BRING TO THE BOIL. REDUCE HEAT TO LOW; ALLOW TO SIMMER FOR 5-8 MINUTES OR UNTIL MIXTURE HAS THICKENED AND REDUCED TO A GLAZE. (IF NOT USING SUGAR, ALLOW TO REDUCE FOR 12-15 MINUTES ON LOW HEAT).