Introduction: This meme contains a quote from Christopher Hitchens.
Key Facts: The line can be found on page 64 of Hitchens’s book God is Not Great. Hitchens larger argument may well be worth looking at in another post. For purposes of this discussion, however, we are focusing on the use of this meme.
Text: “One must state it plainly. Religion comes from the period of human prehistory where nobody had the smallest idea what was going on.”
Comments: In itself, this meme does not clearly present an argument. It seems fair to suggest, however, that the meme is commonly used to discredit religious thoughts. So, we will focus on the prospect of using the meme to generate an argument in opposition to religion. This will necessitate reconstruction of a missing (or implied) assertion.
Statements: The very first sentence contributes little to the point except perhaps a sense of urgency. If we add an implied conclusion (represented in square brackets), this argument has two statements.
 One must state it plainly. Religion comes from the period of human prehistory where nobody had the smallest idea what was going on.
[] [Religious beliefs are false.]
Discussion: This argument raises the following issues; genetic fallacy, micro-reasoning, missing assertions.
Genetic Fallacy: Insofar as the argument uses the origin of religion as a reason to reject the truth of religious beliefs, it is likely a good example of a genetic fallacy.
Micro-Reasoning: As with many meme, the reasoning here suffers a bit from its brevity. In this case, the meme hints at an unstated conclusion, perhaps even pointing to one not entirely consistent with that of Hitchens original text.
Missing Assertions: This meme contains only one line. If it suggests an argument, as I think it does, that argument contains at least one missing assertion (in this case, a conclusion).
Diagram: This one is pretty simple.
1 -> 
Evaluation: There are two items to evaluate in this argument. The truth of premise 1 and the relevance of the inference. The argument comes up short on both counts.
Premise 1 is questionable at best insofar as it takes religion to be a primitive (and erroneous) effort to explain the world in the absence of reasonable scientific methodology. It isn’t clear though, that the point of religious institutions and or mythic narratives of ancient people is to explain objective phenomena. Neither is it obvious that ancient people’s were ignorant about the world around them. Of course, the meme itself doesn’t entirely make it clear to whom Hitchens refers when he is talking about prehistory, but at least some peoples with not actively recording their own history had a quite sophisticated understanding of many things. Did they understand the details of modern chemistry or physics? No. But that hardly qualifies as not having “the smallest idea what is going on.”
The inference from 1 to  provides no support for the conclusion. This is a classic genetic fallacy. If there is any reason to suppose any given religious tenet is wrong, it is not because of its origins.
Final Thoughts: I can think of two contextual problems that could undermine this analysis; my construction of the argument may not be representative of Hitchens’s own intent and it may not be representative of the specific intent of those who circulate the meme.
Hitchens’s intent: Here, I think the solution is simple. It doesn’t really matter. The original context of the quote has been jettisoned in the production of the meme. People circulate the meme itself without necessarily attending to its source. It’s worth keeping in mind that the meme itself doesn’t present Hitchens’ full argument on the history of religion or the significance of that history in polemic dispute, but that should not stop us from addressing the significance of the meme itself as it is circulated about the net.
Intent of Those Circulating the Meme: Here we come back to the one sentence nature of this meme (and it should be noted that other versions include more wording). It’s almost tempting to suggest that this isn’t an argument at all, because it doesn’t draw a conclusion from a premise. I do think it’s fair to suggest that the meme is normally offered with the intent to discredit religion. One has only to formulate the missing conclusion. In effect, this takes the meme to be an expression of an argument against religion by those circulating it. If someone circulates the meme for other reasons, then presumably, this entire analysis would not apply.