Hunter-gatherer bands do not have chiefs. Looking at the Wikipedia article for "Tribal chief" it says "Historically, tribal societies represent an intermediate stage between the band society of the Paleolithic stage and civilization with centralized, super-regional government based in cities." I couldn't put it better.
Even with regards to Indian chiefs, and it's not hard to see how there are misconceptions about them if they're still referred to as "Indians", modern anthropology acknowledges that European notions about Indian bands and tribes in the 15th and 16th century were often wrong. Europeans saw parallels of European society in the New World which weren't there (of course there were different kinds of societies in the Americas, from Montezuma's Aztec empire, to humter gatherer bands).