Mix dressing ingredients together in a small bowl. Refrigerate for 30 minutes.
Spoon 3 tablespoons of dressing into a large bowl. Add diced chicken and toss together to combined. Add in shredded romaine, Parmesan cheese, and croutons and toss together.
Grab a large plain wrap. Place half of the mix in the center of the wrap. Fold in the side edges and then fold the bottom edge over the center and tuck under the lettuce. Roll wrap over to seal. Make a second wrap with the other half of the salad mix.