Shred or chop the chicken, celery, red onion, grapes, walnuts, and parsley. Whisk together the dressing ingredients in the bottom of a large bowl.
Add the chicken and other ingredients and toss everything together. Give it a taste and add more salt as needed.
Heat a burrito-sized wrap or tortilla to make it more pliable by covering it with a damp paper towel and microwaving it for about 10-20 seconds. Place it on a clean flat surface. Add a layer of greens on the end of the wrap closest to you, leaving at least an inch of space on the sides and bottom edge. Add a heaping half cup of the chicken salad on top of the greens in the center of the tortilla.
To wrap, fold sides of the tortilla toward the middle. Then fold the bottom of the tortilla and tuck the edges of the wrap under. Roll the tortilla away from you to the edge.
Hint: to make shredding the chicken even easier, pulse it a few times in a food processor!