Well, the fundamental flaw in the entire premise is an understanding of the word "chance" as well as what scientists have done in the field of abiogenesis... The entire "answers in genesis" argument is a strawman (amongst many other logical fallacies), so I really don't think it's worth addressing. However, abiogenesis itself is a NEW and exciting field of study. Several strides have been made in that field, but we're in the same stage of understanding as we were on evolution prior to the discovery and understanding of DNA. Also, there is the constant confusion of abiogenesis and evolution that creationists conflate. Again, it's a strawman and disingenuous at best.
For instance, in 2010, Dr. Craig Venter actually used a bacterial shell and wrote DNA for it.
Scientists have created the world's first synthetic life form in a landmark experiment that paves the way for designer organisms that are built rather than evolved.
The new organism is based on an existing bacterium that causes mastitis in goats, but at its core is an entirely synthetic genome that was constructed from chemicals in the laboratory.
(Another variation on the same report.) Interestingly, Venter's work was derived from an earlier 2002 effort to work with viruses and cDNA fragments.
Keep in mind, this is only a synthetic genome, not a truly unique organism created from scratch. Although I am confident that the technology will become available in the future. As has been pointed out, the entire genome wasn't built de novo, but rather most of it was copied from a baseline which was built up from the base chemicals with no biological processes, and then the watermarks were added (still damn impressive since they took inorganic matter and made a living cell function with it). But they are working at building a totally unique genome from scratch (PDF).
This is actually quite an emerging field, so much so that the MIT press has set up an entire series of journals for this. As far as to the purpose of these artificial organisms, most research funded by companies are meant to be for specific purposes that biology hasn't solved yet (such as a bacteria that eats a toxic waste or something). Although, a lot of people are concerned about scientists venturing into the domain of theology.
In terms of abiogenesis, there are many resources to learn more about this. Here is a list of 88 papers that discuss the natural mechanisms of abiogenesis (this list is a little old, so I am sure that there are many, many more papers at this time).
I also found this list of links and resources for artificial life. I cannot verify the usefulness of this since the field is a bit outside my area of expertise. However, it does seem quite extensive.
EDIT TO ADD: Now we have "XNA" (a totally synthetic genome) on the way.
One can argue that no one has managed to just let an experiment "sit and stew" resulting in abiogenesis. To the best of my knowledge, that is indeed true. However, since we don't know what really led to abiogenesis yet, the list of 88 papers (and many more) are the best framework we have towards understanding that. In the meantime, letting something "sit and stew" may be an experiment beyond the scope of human endeavours. Hence why we accelerate our understanding with the various other experiments.
Even though I said I wouldn't address the strawman, I guess I must since it's so central to the caricature you seem to have in your mind of abiogenesis and evolution. Consider the below "supplemental material" not central to the answer, but still important to understand if you have any hope of actually understanding the answer.
A bit of an essay about "chance" because I have it handy. I have been informed that quoting it here is not appropriate, so the two specific items are #9 and #11 on the list. (The page may sound somewhat rude and insulting, so keep in mind it was written for a different audience and purpose. And the author is British, and they do have a way with words.) Additionally, it addresses "figures" and "calculations" that creationists frequently use. By the way, it should be telling that all the creationist arguments are the same predictable ones that show up repeatedly with no new information. It's so telling that many individuals have written extensive replies, to the common and asinine objections of creationists.
And even more reading for your education:
Abiogenesis is the field of science dedicated to studying how life might have arisen for the first time on the primordial young Earth. Despite the enormous progress that has been made since the Miller-Urey experiment, abiogenesis is under constant attack from creationists, who continually claim that the origin of life by random natural processes is so unlikely as to be, for all practical purposes, impossible. Following are some articles that challenge this claim and demonstrate the fundamental misconception at the core of the creationists' arguments.
Lies, Damned Lies, Statistics, and Probability of Abiogenesis Calculations
How likely is it that even a single bacterium could form by chance in the primordial sea? Not very likely, that's for sure, and creationists have been only too happy to provide ludicrously huge numbers purporting to be the odds against such a thing. However, even if these calculations are correct, they are irrelevant, as modern theories of abiogenesis require nothing of the kind to happen. This article briefly illustrates what abiogenesis really is and shows why the creationists' probability calculations do not matter.
Borel's Law and the Origin of Many Creationist Probability Assertions
Creationists have asserted that a statistical principle called "Borel's Law" mathematically demonstrates that abiogenesis is impossible. This article explains what Borel's Law is and shows that Borel himself clearly understood that his law was not relevant to the probability of the origin of life.