I did a thread on Alvin Plantinga's religious epistemology, which is related to this idea, on /r/DebateReligion a couple of weeks ago. This is what I wrote:
The purpose of this thread is to discuss Alvin Plantinga's Reformed epistemology. I'm an atheist and I have read most of Plantinga's books and several responses to his work.
Alvin Plantinga is a central figure in the school of thought called Reformed epistemology, which emphasizes the alleged rationality of believing in God without evidence. There are two arguments that serve as the basis for Reformed epistemology: the argument from the self refutation of evidentialism and the argument from examples of beliefs that are justified without evidence. I am not going to go into these in detail here.
Externalism
Arguably the most important thing to know about Plantinga is his approach to externalism.
Externalism is an epistemological position maintaining that we don't need to have internal access to the grounds of a belief for it to be warranted (or "justified," depending on how we define our terms). The idea of externalism was originally intended as a way of thinking about justification that avoided epistemic skepticism: "We can't refute the skeptic, so let's focus on doing experiments on our perceptual apparatus and showing that it works reliably from a third person point of view at least."
Plantinga's twist was to take externalism and use it as a justification for religious belief. Since we usually don't have access to the grounds of our warranted beliefs, it's unfair to ask the religious believer to justify his belief in God - we can only hope that the beliefs our cognitive faculties produce in us line up with reality.
Christianity and Warrant
This last point about cognitive faculties, however, leads Plantinga to the conclusion that which side is warranted depends on which side's cognitive faculties are functioning properly in reality, i.e., whether theism is warranted turns on whether theism is true. This implies that atheists cannot merely criticize theism as unwarranted, since it is warranted if it is true. Atheists have to use metaphysical arguments to disprove the existence of God.
Plantinga also thinks that there is an asymmetry between theism and atheism. If theism is true, then belief in theism is likely warranted, since God would be likely to provide us with a reliable faculty for knowing him. However, if atheism is true, then atheism is probably not warranted, because on atheism our cognitive faculties are the result of blind, unguided evolution, and therefore probably unreliable. (This is where the EAAN fits into Plantinga's overall system.)
Recap
Let's review the claims Plantinga makes that I've covered:
Evidentialism is self refuting and subject to numerous counterexamples (technically Plantinga attacks classical foundationalism, but let's not worry about that here).
It's unreasonable to require the believer to have evidence that God exists, since most of our beliefs aren't supported by evidence.
Instead of depending on evidence, the debate about whether theism is warranted turns on whose cognitive faculties are functioning properly, which turns on whether theism is true metaphysically.
There is an asymmetry between the two sides in this debate, since naturalism implies that all of our beliefs are probably unwarranted.
I have my own objection to Plantinga's system, but I'll stop here and let people discuss his ideas first.