Fortunately, the Chiefs don't use a stereotypical chief logo, or this would be really bad. I think the only stereotypes they use are the arrowhead logo and Arrowhead Stadium. These aren't good, since they imply Indians still live in the Stone Age, but they're relatively minor.
Of course, the image below was the Chiefs' primary logo from 1963-1971, according to one website. It shows what was going through the owner's mind when he named the team. An Indian chief as a loincloth-wearing, tomahawk-waving savage.
You can practically trace the history of the chief stereotype from this example. "Chief" Bartle got the stereotype from an old Western movie or a product label, or perhaps directly from a Wild West show. The Kansas City Chiefs got the stereotype from "Chief" Bartle. Now some guy who was a Chiefs fan as a boy is repeating the stereotype in TV commercials, cartoons, or comic books.
For more on the subject, see Team Names and Mascots.