There are no direct train connection from Chennai to Madikeri. Travel by train to Mysore from Chennai first and then take a bus or cab from Mysore to Madikeri.
There are a couple of daily express trains from Chennai Central (Station Code: MAS) to Mysore Junction (Station code: MYS) via Bangalore City.
Kaveri Express (daily): Train Number : 16222 (Chennai-Mysore) & 16221 (Mysore to Chennai).
Shatabdi Express (daily*) :Train Number : 12008 (Chennai-Mysore) & 12007 (Mysore to Chennai).
Bagmati Express (weekly): Train Number 12577 (Chennai to Mysore) & 12578(Mysore to Chennai).
Mysore Express (weekly): Train Number 22682 (Chennai to Mysore) & 22681(Mysore to Chennai).
*no operation on Wednesdays.
Check irctc.co.in for reservation,schedules and ticket fare.