What do Atheists think about this evolutionary conundrum?

That "conundrum" was solved long ago. DNA evolved from a simpler molecule, probably RNA, that did not need a cell to replicate.

I don't know why that seems implausible to you, but it's what happened. RNA itself probably evolved from a simpler precursor, such as a peptide nucleic acid. A deoxyribozyme can both catalyze its own replication and function to cleave RNA -- all without any cell.

"kind of like the chicken and egg argument"
The answer to this is the egg, this was solved 300 years ago.

"Of course there' the RNA theory, but it doesn't seem plausible yet to me"
With your complete lack of education in molecular biology, I wouldn't expect it to. But your opinion is irrelevant isn't it? Magic is obviously more plausible.

Remember: the alternative to life forming under natural laws is that your god was too stupid to figure out how to do it under the very laws he created. Scientific laws have never been witnessed to be broken even momentarily, so if a god exists he obeys the laws he created. To say that life requires magic, is to spit in the face of your god.

Looks like you've been fed a pack of lies by some creationist organization. There is no conundrum. A simple prokaryotic cell does not need DNA. The simplest cells are just lipid layers with some simple structures inside.

This is an abiogenesis conundrum, not an evolution conundrum. Abiogenesis is a process which could cause the spontaneous formation of incredibly basic life, which could then diversify into everything we know through evolution. Evolution doesn't even try to discuss where DNA came from. That is not in evolution's territory. Evolution stands alone without abiogenesis. Theistic evolution is the belief that God created the first life, and then used evolution to evolve said life.

Also, not everyone who accepts evolution is an atheist. Not that I'm offended.

"There might have existed a protocell of some sort..."

You just answered your own question.

In the case of the chicken and the egg thing it was the egg of course. Birds descend from reptiles, and reptiles lay eggs. Go far enough up a chicken's bloodline and you'll find something that wasn't a chicken that still hatched from an egg.

Biology is that way. -->

Or were you hoping to get a bunch of "I don't know" answers from atheists and pats on the back form fellow believers? I think you'll find that some atheists (not all) actually ARE evolutionary biologists and can answer this question quite proficiently.

You are making an incorrect assumption. DNA USES the cell to reproduce itself, but the original forerunner to DNA was assembled by chance combinations of simple molecules. By its very structure chemically, the DNA molecule will reproduce under the right conditions. It does not NEED the cell to do so.

This question should be better asked in science. But since I work in biotechnology I'll give you the gist of the explanation. In the cells regulatory function there are three main parts DNA, RNA, and proteins. DNA is simplistically speaking the memory bank of the cell's hereditary instructions, and proteins and their enzymes make things happen in the cells. RNA is the intermediate, but can do lots of functions. RNA in some viruses is the coding capacity. RNA does have the capability to carry its own coding capacity (transposons, dsRNA, and several other elements of the cell use this capability) and can be used enzymatically. It is the transition state between DNA and proteins. RNA isn't as stable as DNA and so DNA is therefore the only molecule used in living things, but it isn't inconceivable that primitive forms of life would have been RNA based molecules until by chance a DNA molecule was formed (which isn't all that different from RNA as it differs by an OH group). This would have been a random dance of molecules and by the time of the first bacteria DNA would have probably existed from some time in the primordial seas.

It started with prokaryotic cells which are cells without a nucleus, and they had simple DNA which had developed over time until these cells were produced. Since DNA is just made up of 4 types of protein molecules then there was nothing to stop these molecules from existing outwith a cell environment and as they joined together cells were then formed.

"Of course there' the RNA theory, but it doesn't seem plausible yet to me."
Are you a biochemist? I'm not, so I do not really know how plausible it is, but the scientists have not ruled it out. In the past when we have found something we do not understand, natural causes have been the explanation. I find it likely that the same is true in this case.