Many successful sites without chat. Bitzino, coinroyale, coinroll and satoshibet to name a few. Chat is nice but don't make it seen like a deal breaker.
It is for me. If there is a dice site with chat and one without, I will go to the one with chat. Also if I get to know some of the people on chat it is much more fun than randomly betting lonely...
But chat is not necessary for a site to be successful, I just prefer it