The best and shortest route will be to first take a Chennai to Bangalore flight (1 hour max). From there, Chitra Durga is a 3 hours' drive (200km) -> Hubli (200km) -> Panjim (200km). A total of around 1000 km. It took almost 20 hours for me to reach Chennai from Goa through this route, with 3 hours of break.
You can try typing Chennai to Goa by road in the search box above, to find driving directions, places to eat along the way and even the petrol pumps, atms and places to visit on the route. Planning a road trip was never this easy. Give it a spin!