Jiyeoun and I finally had "pearl tea". The Lonely Planet guide book describes it as "sweetened tea with chewy black balls of tapioca at the bottom." It's served in a plastic cup with a tight seal and thick straw. The Chinese word for it is zhēnzhū nǎichá. Don't ask me to pronounce it. Jiyeoun ordered for me.
The tea cost 45 TWD ($1.40 USD) at a roadside stand in Danshui. (More on Danshui later.) The tea was good. It was not as sweet as I expected. It tasted like Earl Grey with milk and balls of nut jelly in it. It was surprisingly filling for tea. I'd rate it as better than average. I'm certainly going to try it again somewhere else. I'm sure there are dozens of variations. The streets are littered with pearl tea stands.