Heat a large skillet over medium heat. Add a flour tortilla and blister it on one side, then turn it over. Scatter cheese on top and cook one minute.
Remove to cutting board. Top the tortilla with 1/4 cup salsa, spreading it gently with the back of a spoon to the edges. Top with 1/2 cup chicken, then roll tortilla into a log. Let stand a minute before cutting. Repeat with remaining ingredients to make a total of four tortilla logs. Cut pinwheels into 1/2-inch slices and arrange on platter.