The first teapot ever was invented in China. This old relic dates back to some time before 1513. As of 2008 it is being held in the Flagstaff House Of Teaware in Hong Kong. It was likely first created by a Chinese monk.
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Various sources report the first teapots appearing during the Sung Dynasty (960-1279) or the Ming Dynasty (1368-1644), but virtually all agree they first came from the YiXing (pronounced "ee-shing") region of China, about 120 miles northwest of Shanghai. There, a purple clay known as "zisha" was formed into the first small pots.
These teapots were made to brew only one or two servings of tea, which was drunk directly from the spout. At the time, people carried their own personal pots for brewing and drinking tea.
(source - http://www.go-star.com/antiquing/when_was0208.htm )