Depends on how you read it.
There was certainly a time when the consensus of Christian thinking was that the Bible clearly indicated that the Earth was fixed and at the center of the universe, and that man, God, and the angels were the only thinking things. This would obviously preclude aliens.
Over time, the consensus of Christianity has left this view, and I don't think a consensus has really formed over whether the Bible allows for or excludes other intelligences. Many of the fundamentalists claim that this would cheapen man, and so there are no aliens (the same reasoning they use against evolution establishing man as an animal). Many of the more liberal see no such exclusion. I imagine this will be debated right up until we find alien inteliigence, at which point it will be the "mud people" argument all over again.