DS was in that phase when he was 4yo. Everyday was chess day. He was lucky that his Kindy teacher allowed him to play chess on the iMac on days when she was in the classroom.
Back than he read many chess books. He has a few favourites:-
-How to Beat Your Dad at Chess by Murray Chandler
-Chess for Kids by Michael Basman
-Internet-Linked Complete Book of Chess (Usborne Internet-linked Reference)
by Liz Dalby

He also visited chess sites like http://www.chesskids.com/

Joining the school's chess club (if any) is good as the child will get to play with different players.

Too bad DS doesn't even look at chess now.