The Chiefs have many rivals in their history from the National Football Conference.
Green Bay Packers
The Green Bay Packers as rivals for Kansas City predates the NFC/AFC and instead resides in the AFL/NFL pre-merger days of Chiefs football. The rivalry existed primarily due to two overwhelming factors.
First, Vince Lombardi and Hank Stram were two of the biggest names in coaching, and also two of the most successful coaches in professional football in the 1960s. As such, there was some natural push-and-pull to the way the teams were talked about writ large.
Second, and more obviously, was the teams’ meeting in the very first World Championship game, Super Bowl I, at the conclusion of the 1966 season. While both franchises would fall off significantly after the 1960s ended, the rivalry nonetheless existed after the championship clash.
The Chiefs lead the all-time series 7-5-1.
Dallas Cowboys
The roots of the Chiefs-Cowboys rivalry lie in the franchise’s inceptions more than anything else. Both teams were founded by Texas businessmen—giants of industry. They were founded in the same year (chartered in 1959 and began play in 1960). Finally (of course), both had their origins in professional football in Dallas.
As the Dallas Texans attempted to kick off not only their franchise but also the American Football League, they not only battled with the Cowboys for fans but also players. Traditionally, Lamar Hunt lost many of these battles due primarily to the NFL’s larger profile, more established game, and greater financial resources. The Chiefs were outbid, essentially, for a number of players drafted by (or signed as free agents by) the Cowboys, including Hall of Famers “Dandy” Don Meredith, “Mr. Cowboy” Bob Lilly, and Roger “The Dodger” Staubach.
Hunt, of course, moved the team to Kansas City prior to the 1963 season, but the rivalry persisted for years beyond that.
The Cowboys lead the all-time series 7-4.
Minnesota Vikings
Like the Packers rivalry, the Chiefs rivalry with the Minnesota Vikings throughout the 1970s was rooted in their championship tilt which kicked off the decade, as Kansas City defeated the Vikings 23-7 in Super Bowl IV to conclude the 1969 NFL season. The Chiefs victory shocked Minnesota, and the world, as the AFC was still considered an inferior conference due to the longevity of the NFL/NFC as a league. Kansas City was not even the best team in their division in the standings that year (finishing second in the West).
Nevertheless, the Chiefs dominated the Vikings and the rest was history. The Chiefs and the Vikings had many battles over the years, and they always seemed to have just a touch of extra flair by comparison to other AFC-NFC clashes.
The Chiefs lead the all-time series 8-5.