Yes, for many people regarding many topics it would. If 'free speech' really meant what it said, then it wouldn't have a great effect. I should hope not.
Different people have different levels of comfort in the freeness of their communications.
I don't think that's necessarily a chilling effect. I hope not. In a totalitarian state, it definately would, but I believe the net can be a great tool against totalitarianism. To some extent. I personally do not think so.