Giller was born in Jacksonville, Illinois, on 8 July 1918.[4] He grew up in White Hall, Illinois. He attended Kemper Military School, MO for his last two years of high school. In 1940, he obtained a Bachelor of Science degree in Chemical Engineering from University of Illinois, where he was a member of Gamma Zeta chapter of Alpha Tau Omega fraternity. He worked for Sinclair Oil Refining Company in Houston, TX until the advent of WWII.
Giller served as a P-38J Lightning[5] and P-51D Mustang fighter pilot with the 343d Fighter Squadron, 55th Fighter Group, for the United States Army Air Force during World War II. His P-38 and all four of his Mustangs were named "The Millie G", for his wife, airline stewardess Mildred, and coded 'CY-G'.[6][7][8] He served as commanding officer of the 343d, and later, as deputy commander of the 55th.[9] He had three confirmed kills, including a Messerschmitt Me 262 over Munich on 9 April 1945. Giller also had six credited ground kills and two damaged.[10] He was wounded when his cockpit was hit by flak over Munich on 16 April 1945 – he flew two hours to the UK with one arm.[11]
Between 1954 and 1959 he was the Special Assistant Director and later the Director of the Research Directorate, Air Force Special Weapons Center, Kirtland Air Force Base, New Mexico.[12]
Giller died in October 2017 at the age of 99.[13] He was married to his wife, the former Mildred Schmidt, of Grants Pass, Oregon, for 69 years until her death 16 November 2012.[14] They had five children.[15]