The correct chronological sequence of their visits is:

III, I, IV, II

1. Megasthenes (IV) - Megasthenes, a Greek ambassador, visited India during the reign of Chandragupta Maurya in the 4th century BCE. He wrote detailed accounts of Indian society and culture in his work called Indika.

2. Fa-Hien (I) - Fa-Hien, a Chinese Buddhist monk, traveled to India during the Gupta Empire in the 5th century CE. He journeyed through various regions in India, collecting Buddhist scriptures and studying Buddhist monastic life.

3. Hieun-Tsang (IV) - Hieun-Tsang, also a Chinese Buddhist monk, visited India during the 7th century CE. He traveled extensively across India, studying at famous Buddhist centers and collecting Buddhist scriptures. His accounts provide valuable insights into the political, cultural, and religious aspects of ancient India.

4. I-Tsing (II) - I-Tsing, another Chinese Buddhist monk, came to India in the 7th century CE. He visited many prominent Buddhist centers and universities, including Nalanda, and collected important Buddhist texts. His writings contribute to our understanding of Buddhism and the intellectual and educational environment in ancient India.

Therefore, the correct chronological sequence is III, I, IV, II.