Herein, a slightly enhanced version of extended Huckel molecular orbital theory is applied to demonstrate the spontaneous distortion of 1,3,5,7-cyclooctatetraene from a perfect octagon, a consequence of the Jahn-Teller effect. The exercise is accessible to students who have been introduced to basic quantum mechanics and extended Huckel molecular orbital theory and is easily implemented with widely available algebraic manipulation software such as Maple or Mathematica. This exercise is suitable for inclusion in the physical chemistry curriculum at the upper-level undergraduate or introductory graduate level. (Contains 7 figures.)