Dice the celery and green onion. This ensures they’ll distribute evenly throughout the filling, adding just the right amount of crunch and flavor to every bite. Set the diced vegetables aside for later.
Scoop the avocado into a medium mixing bowl and use a fork to mash it until smooth. It’s okay if there are a few small lumps for added texture. Add the mayonnaise and a pinch of black pepper to the avocado, then stir until everything is fully combined.
Add the shredded cooked chicken to the avocado mixture. Gently fold it in with a spatula, making sure the chicken is evenly coated with the creamy mixture. This will serve as the flavorful base for your pinwheels.
Lay out the three tortillas on a flat surface. Divide the chicken avocado mixture evenly among the three tortillas, spreading it out in a thin, even layer. Sprinkle the diced celery and green onions over the top of each tortilla to add freshness and texture.
Starting at one edge of a tortilla, roll it tightly into a log shape. Take your time to ensure the roll stays compact, which will make slicing easier and keep the filling from spilling out. Repeat with the remaining tortillas.
Wrap each rolled tortilla tightly in plastic wrap. Place the wrapped rolls in the refrigerator to chill for at least 1 hour. This step helps the flavors meld together and makes the pinwheels easier to slice.
When ready to serve, remove the plastic wrap from the rolls. Using a sharp bread knife, slice each roll into 1-inch pieces. Trim off the uneven ends (and feel free to snack on them while you work).
Arrange the sliced pinwheels flat on a serving platter. They’re ready to enjoy as a snack, lunch, or appetizer.