Take a flight and go

There is no direct flight. Best option is to fly Beijing (China) and there is direct flight to Ulan Bator (Mongolia).

Other option:

Chennai -> Bangkok (Thailand) -> Beijing (China) -> Ulan Bator (Mongolia).

Chennai -> Singapore -> Beijing (China) -> Ulan Bator (Mongolia)
There are some connections from Seoul -> Beijing -> Ulan Bator.

Sorry I am not sure about the distance!

It is not advisable to travel alone to mongolia if you have not travelled there before or have any local contacts.

Contact any good travel operator to get flight and hospitality details before the journey.

distance from chennai to ulan bator (capital) is approx 4580 Kms.

Why do u wanna go to mongolia