In a large bowl, combine the shredded chicken, mashed avocado, cherry tomatoes, lettuce, and shredded cheese. Mix well until all ingredients are evenly distributed.
Drizzle the ranch dressing over the mixture and season with salt and pepper. Stir gently to combine.
Lay a tortilla flat on a clean surface. Spoon a generous portion of the chicken and avocado mixture onto the center of the tortilla.
Fold in the sides of the tortilla, then roll it up tightly from the bottom to the top. Repeat with the remaining tortillas and filling.
If desired, slice each wrap in half diagonally and serve immediately. For a crispier wrap, grill the filled wraps on a skillet over medium heat for 2-3 minutes on each side until golden brown.