Step 1: Recall the history of Mysore Palace.
The Mysore Palace, also known as Amba Vilas Palace, is one of India's most visited monuments and one of the most magnificent royal palaces in the world.
Step 2: Identify the ruling dynasty.
The Mysore Palace is associated with the Wadiyar dynasty (also spelled Wodeyar), who ruled the Kingdom of Mysore for centuries. The current palace was built during the reign of Krishnaraja Wadiyar IV in the early 20th century.
Step 3: Rule out other dynasties.
Cholas, Kadambas, and Chalukyas are ancient dynasties unrelated to this palace.
\[ \boxed{\text{Wadiyar dynasty}} \]