While "Christianity" is a bit of a misnomer, since there is not much correlation between christianity and any given philosophical school, I would agree that much of Rand's philosophy agrees with what a lot of Christians espouse, particularly among the evangelical crowd in America. Asimov likely knows more about objectivism than I, so he is free to correct me on this, but here are the basic similarities as I see them.
Objectivism holds, first of all, that there is a mind-independent reality and that individuals are in contact with this reality through sensory perception, something that most Christians would absolutely insist upon against fervent opposition from many modern schools of thought. Creationism in particular is tied to the notion that the universe exists independently of human thought, and that one can therefore make absolute statements about its nature and origins. Rand also felt that humans gain objective knowledge from perception by measurement, and by forming concepts that correspond to natural categories by measurement omission. You would see some opposition to the notion that objective knowledge is generated by the scientific method, but mostly from either very conservative or very liberal Christians- mainline Christians would not object. So the basic assumptions are for the most part in line with each other, though Ayn would fervently object to the conclusions drawn from them in some cases.
Moving on to moral theory, the proper moral purpose of one's life according to Rand is the pursuit of one's own happiness or "rational self-interest"; she therefore encourages laissez-faire capitalism, which she insists is the only way to create genuine balance. Here she does contradict two millenia of church beliefs, which encourage love, mercy, and sacrifice for the well-being of others. However, the American Christian Right would fully agree with her, as evidenced not only by their open support of capitalism and political libertarianism, but also in more subtle ways- the adoption of "personal salvation" as the primal goal, and a general interest in eschatological matters and hell doctrine, all of which imply that personal wellbeing and self-interest should be the guiding factor in one's decision to live a Christian life. This is not to say that Christianity or even fundamentalism directly support or denounce objectivism. Neither Calvinists, Roman Catholics, nor liberal theologians in general would support Rand's theories in their entirety, so by majority rule at least Christians are not objectivist. But I suspect there are a considerable number of people who hold both sets of moral information in high regard.
EDIT to add a side note: how can one be diametrically opposed to Christianity? Christianity is frequently diametrically opposed to itself.