Bake fries according to package instructions for the entire bag.
While fries cook, prepare to balsamic reduction. Add vinegar to a heavy bottomed saucepan. Gently, bring to a simmer and allow the vinegar to reduce by half. This typically takes about 20-25 minutes. Remove from heat and allow it to cool for 5 minutes.
Remove fries from the oven and lightly sprinkle with salt.
Pour fries in a large bowl. Add pesto and gently toss to coat.
Place fries on a serving dish. Top with chopped cooked chicken.
Drizzle with balsamic reduction. Grate fresh Parmesan on top of the fries.