Detailed Explanation:

Vijayalaya founded the medieval Chola Dynasty around 850 CE by capturing Thanjavur from the Muttaraiyar chiefs and establishing it as his capital.

Karikala was an early Sangam-era Chola king (c. 2nd century CE), not the founder of the medieval dynasty. Aditya I was Vijayalaya's son who expanded the kingdom, and Rajaraja I was a later emperor who built the Brihadeeswara Temple.

Therefore, Vijayalaya being the founder of the medieval Chola Dynasty makes Option 1 the correct answer.