Kenzan Island is an island somewhere in Paradise, where the Tehna Gehna Kingdom (テーナ・ゲーナ王国,Tēna Gēna Ōkoku?) is located.
This place seems to be the homeland of the Longarm Tribe, having Chinese-like constructions and valleys between mountains that have a sword shape and the island itself is surrounded by whirlpools. This is where the Longarm Tribe had taken Brook and put him on display. While the Longarms in Kenzan witnessed the living skeleton through in his cage, Brook was able to obtain a newspaper to learn of Luffy's exploits. Due to the fact that there was an audience to look at Brook, it seems fairly well inhabited.