Hi, Don. I may be reading this completely wrong. But it appears to me, from this article that it was in 2003:
The Chiefs went 13-3 in 2003 and their offense, considered by many as one of the most powerful of all time, helped make Kansas City again a favorite to win Super Bowl XXXVIII. After starting 9-0, the Chiefs lost to the Cincinnati Bengals in their tenth game following a "guarantee" by Bengals wide receiver Chad Johnson.
Maybe I've read that wrong, but I was looking at the "after starting 9-0" part.