We cannot conceive of a world without communication. God has chosen the art of language, particularly spoken language, as His way of developing relationship with His creation. God's value of language, His history with it, and various biblical passages all indicate that there will be a language in heaven, though we do not know what that will be like.
A language will be spoken in heaven, and if we accept that the multiple languages we experience on earth are all imperfect representations of reality, none of them can be the language we will speak in that perfect place. Although the Bible does not address this directly, there are three passages that imply both the use of language and a significant improvement upon it. Isaiah 62:2 indicates that Israel will "be called by a new name that the mouth of the LORD will give," while Revelation 3:12 indicates that Jesus himself will have a new name. Finally, Revelation 2:17 says, "To the one who conquers. . . I will give him a white stone, with a new name written on the stone that no one knows except the one who receives it." Each of these passages indicates a "new" naming system, and a very special one at that.
What heaven will look like and feel like perhaps provides the largest blank canvas for the creative mind that can be found. The declaration that heaven is like "What no eye has seen, nor ear heard, nor the heart of man imagined" (1 Corinthians 2:9) gives us both enormous freedom to imagine and the knowledge that we will never quite understand while here on earth. As such, we may believe that God will allow language, along with every other part of life, to be re-perfected, but we have no idea what that will actually look—or sound—like.