This is for any division in football (I, II or III).
Why is this relevant?
Well, the game that came closest to accomplishing this task last season?
The Texas Bowl. Navy was flagged twice for 10 yards. Mizzou was not charged with a penalty at all.
(h/t: Dr. Saturday)
Update at 11:06 Pacific: According to the AP Top 25 Twitter feed, the last game with no penalties at all took place in 1986. It was Army-Navy.