Cut 2 strawberries into pieces and place in a small bowl or cup; use a fork to mash to a pulp.
Into a small jar, add balsamic vinegar, oil, mayonnaise, sugar, pinch of salt and mashed strawberries; screw lid onto jar; shake vigorously for several seconds; refrigerate until needed (up to 3 days.) Shake well before pouring.
Into each salad bowl, layer lettuce, chicken and sliced strawberries.
Sprinkle with sunflower kernels; sprinkle with cheese.
Shake salad dressing very well; pour desired amount over salad (up to 1/2 of the dressing.)
Serve immediately. Cover and refrigerate leftovers.