From wikitravel:
Regular pax ship services are available to Port Blair from Chennai. There are 3 to 4 sailings every month, The voyage takes about 50 to 60 hrs & the ship normally berths at Port Blair for about 2 to 4 days.
Schedules & tariffs can be obtained from:
Shipping Corporation of India Ltd., Jawahar Building, Rajaji Salai, Chennai – 600 001 Tel:...
more... 044-25231401to 9, 25225835,25231407.
The Deputy Director of Shipping Services, A&N Administration, 6, Rajaji Salai, Chennai – 600 001 Tel: 044-25220841 , 25226873
Estimated Fares: Name of Vessel and fare per berth (Tourist/Non Islanders in INR)
M.V.Nicobar 5,880.00
M.V.Nancowry 4,860.00
M.V.Swarajdweep 1,510.00 to 3,870.00
M.V.Harshvardhana1,510.00 to 5,880.00
M.V.Akbar 1,310.00 to 5,880.00