Since those years, the Chiefs have had plenty of very good teams, most notably in the 1990's under Marty Schottenheimer. Unfortunately, Kansas City hasn't been able to win another Lombardi Trophy, always finding a way to screw it up.
However, plenty of good teams played those seasons only to fall short whether it be because of an awful kicker, a great kicker gone bad for a day, or plain bad coaching. Of course, they also ran into some great squads.
So which one was the best not to win it all? Was it the 1971 Chiefs led by Len Dawson, Hank Stram and a defense featuring players such as Emmitt Thomas, Bobby Bell and Willie Lanier?
How about the 1995 team which went 13-3 and was the No. 1 seed in the AFC before losing to Jim Harbaugh and the Indianapolis Colts in a stunning upset? Same could be said for the 1997 squad, which again was 13-3 and the top seed only to be defeated at home in the Divisional Round.
I'm going with the 1971 team, but personally the one which hurt the most was 1993. I'm not old enough to have seen the glory years, but as a kid watching Montana get knocked out in Buffalo, I remember crying and knowing it was over.
What say you? Which team was the best to fall short in Kansas City history?