This paper critically examines what Nicholas Wolterstorff has to say in Divine Discourse in response to the two questions in the title. It tries to show that his argument for the conclusion that God can have the obligations of a speaker is defective. It also tries to show that his argument for the conclusion that some actual person is entitled to believe that God has spoken to her is incomplete. The paper's conclusion is that Wolterstorff's arguments fail to establish, or to provide strong grounds for accepting, a positive answer to either of the questions in its title.