There are actually a few, especially in Pingtung County. The main language is Mandarin Chinese. Taiwan used to be part of China, and most Taiwanese people have Chinese ancestry. Schools and businesses in Taiwan use Mandarin, so it's essential here. However, Taiwan’s Mandarin is slightly different from China’s Mandarin (think American English vs. British English), and uses the traditional method of writing Chinese characters instead of the simplified version that China uses.
Taiwanese is also a common language (also called ‘Hokkien’), mostly heard in rural areas of Taiwan. It comes from a part of China that many rural Taiwanese people came from many centuries ago. In Pingtung, almost everyone can speak Taiwanese. But in larger cities like Taipei, the Taiwanese language is uncommon. There is also a language called Hakka, which is spoken by another, smaller ethnic group of people who immigrated from China centuries ago. Pingtung is actually home to some of the most Hakka people in Taiwan.
There are also indigenous languages. While Mandarin, Taiwanese and Hakka have some similarities, indigenous languages are completely different. There are about 15 spoken in Taiwan, each belonging to unique tribes that have lived in Taiwan for thousands of years.