The current storyline of One Piece takes place in the sixteenth century, according to the One Piece Wiki. This is based on Mont Blanc Nolands logbook, which was dated the year 1120 and used a calendar that can be used as a guide to work out the timeline. However, it is important to note that One Piece does not take place on Earth and is set in an alternate world with an alternate timeline. The ships in One Piece match up to those during the 1800s, and Sanji smokes cigarettes, which were first made during the 1820s, leading some to believe that it takes place during the 19th century. However, this is not a definitive answer, and the exact time period is not explicitly stated in the series.