82nd airborne
A United States Army division created for World War I, that would then become America's first Airborne Division during World War II. They saw extensive service throughout the European Theater, including North Africa, Sicily, Italy, the D-Day landings in Normandy, Holland, and the Battle of the Bulge. They are the only remaining true airborne division in the US Army today. (Their WW2-era counterparts, the 101st Airborne, are now an air-mobile division using helicopters, rather than an air-borne division that uses parachutes.)
Their unit patch is a blue circle in the middle of a red square background, with the letters "AA" (short for "All-American") in white in the middle. A blue crest running over the square reads "Airborne".