Shred the cooked chicken to equal about 4 cups (roughly equal to 2 breasts and and 1 thigh) and add to a medium pot.
Stir 3/4 cup of the Caesar dressing and parmesan into the chicken and heat over medium-low heat until warmed, 5-10 minutes - usually about the time it takes to wash and shred the lettuce and prep any other meal items. (NOTE: if starting with hot chicken, simply shred and mix like the cold directions below.)
Divide the chicken mixture evenly between the tortillas and top with a large handful of lettuce and more parmesan. Drizzle a bit more dressing over the lettuce before rolling up and cutting in half.
To Make Cold Wraps (for picnics, lunches, and hot summer nights):
Shred the cooked chicken to equal 4 cups and add to a medium sized bowl.
Stir in 3/4 cup of the dressing and half the parmesan.
Divide mixture between tortillas, top with lettuce and remaining parmesan. Drizzle with more dressing and roll up.
Make Ahead Tip: These are great to make a few hours ahead for dinner or lunch on the go, but they aren't really as good longer than that because the tortilla gets a bit soggy. I found making them the night before for lunches or in the morning for dinner works best.Want low-carb? Don't shred the lettuce, but separate it into leaves and fill the leaves with the dressed chicken, parmesan, and dressing.