The famous Chinese traveller Hieun Tsang visited India during the reign of Emperor Harshavardhana. This question is a part of General Knowledge, focusing on historical visits and interactions between India and other countries.

Let's analyze the options given:

1. Ashoka: Ashoka was an Indian emperor of the Maurya Dynasty, ruling from 268 to 232 BCE. He was known for spreading Buddhism across Asia. Hieun Tsang's visit occurred much later than Ashoka's reign.
2. Samudragupta: Samudragupta was a ruler of the Gupta Empire, which was earlier than Harshavardhana's period. Hieun Tsang visited India after the period of the Gupta rulers.
3. Chandragupta I: Another Gupta ruler, Chandragupta I ruled before Samudragupta and Harshavardhana. Hieun Tsang's travels took place much later, around the 7th century CE.
4. Harshavardhana: Harshavardhana ruled North India from 606 to 647 CE. Hieun Tsang visited India during this period, around the 7th century CE, and his accounts are invaluable for understanding this era of Indian history.

The correct answer is Harshavardhana. Hieun Tsang's travels and interactions have been significant in providing detailed descriptions of Indian society, religion, and culture during Harshavardhana's reign.