Through the 2008 season, the Chiefs have won 3 AFL Championships (1962, 1966, and 1969) and 1 Super Bowl (Super Bowl IV).
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Between 1986-2008, six.
2003: 83-79
1993: 84-78
1991: 82-80
1989: 92-70
1988: 84-77
1987: 83-79