Heat oven to 350°F. Bake biscuits as directed on bag. Cool slightly, about 5 minutes.
In 6-inch nonstick skillet, heat chicken, buffalo sauce and celery over medium heat about 3 minutes, stirring frequently, until hot. Stir in blue cheese.
Split biscuits horizontally. Spoon chicken mixture onto bottom halves of biscuits; top with cucumber slices and biscuit tops.