I don't think we've mentioned anything about God in our talks, have we? Anyway, it depends on how many Gods you are talking about because in Theravada Buddhism, in Buddhist cosmology, there happens to be many realms with these beings and believing in these beings doesn't hinder enlightenment at all. The belief that these realms and these Gods are permanent may hinder it, but the belief in a God may not hinder it.
Some people have the belief that if we believe in a God we will then go to that heaven and live forever. So I feel it would be the belief in permanence and not having responsibility for our own purification that may hinder our enlightenment, by us not making the effort now to purify ourselves.
However in the Bible, in the Sermon of the Mount, it is written that Jesus said, "Blessed are the pure in heart because they shall see God." So it also depends on your perception and idea of God. "Blessed are the pure in heart because they shall see God." The Buddha is recorded to have said, "Do good, avoid harm and purify the mind." So in order to see God or whatever you conceive as the highest, whether it's a personal or impersonal God, (the impersonal law of Kamma), we have to purify the heart. So the question really becomes how do we purify the heart? If we have a belief that we don't have to purify the heart, it may hinder us from seeing either our perception of a personal or impersonal God or becoming enlightened, i.e. free from all greed, hatred and ignorance.