Of all the arguments for God, this one is probably the most persuasive to many who don't want to believe in God. Hitchens and Dawkins, both advocates of the "New Atheism," have admitted that this is the hardest argument to refute. And it is really true, because you quickly get absolutely silly results when you believe that life appeared spontaneously.
The teleological argument is the argument that the universe seems created for the purpose of life -- that there appears to be a design, or fine-tuning in the creation of a universe. This becomes a probabilistic argument, meaning that it quickly becomes far more likely that God exists and created the universe than that it arrived in its present form accidentally.
The atheist will typically argue that given enough time and space, eventually any coincidence is possible and there would be some place somewhere ideal for life. But the fact is that there is a limit to the amount of matter in the universe. There are differing opinions on this, but the general consensus is that there are around 1.0 x 10^80 atoms in the universe.
In comparison to that, we can conduct something known as a Fermi estimation. This is a process where we do not attempt to be precise, but we choose orders of magnitude to estimate just how probable an event is. It turns out that the result of a Fermi estimation might be off my 25%, but it can still be highly instructive when discussing large numbers in comparison. If the odds of natural formation of, say, Earth in a Fermi estimation is 1.0 x 10^40, then we can safely say that the Earth could have happened naturally. If, on the other hand, it is 1.0 x 10^100, we can safely say that it is very unlikely the Earth could have happened naturally. After all, even if we are off my 25%, it still only makes the probability 1 in 7.5 x 10^99 (in comparison to the number of atoms in the universe, which is much, much less).
For the Fermi estimation, we take those things that we know are necessary for life and we calculate how likely they are. Mathematically, we can show that only G-class stars such as the Sun can support life (other stars either have too much UV radiation or no liquid water -- it is impossible to have a place that has both elements of life for non-G-class stars). That eliminates 80% of the stars in the universe, but because it is a Fermi estimation we will look at that like an order of magnitude of 0.1.
We then start collecting these orders of magnitude. Only certain masses of stars work (0.0001). Only certain locations work (0.1). Only certain distances from supernovae (0.01). Only certain distances from the star work (0.0001). Only certain surface gravities work (0.001). Only a certain axial tilt of the planet works (0.1). Only a certain rotational period works (0.1). The separation between water and land (to support life) required a collision in the ancient past (0.1), but of something with a certain mass (0.001) at a certain time (0.01). Just these few elements give us a number 1.0 x 10^21, but this is really just the beginning.
When all of these things are collected, the Fermi estimation for a planet like Earth developing is 1.0 x 10^105. That means that if every atom in the universe was actually a planet, Earth would naturally form by accident (according to our best current understanding) in only 1 universe out of 10,000,000,000,000,000,000,000,000. Long odds, indeed.
And that is just for the conditions for life to have formed with the underlying physical constants of the universe being what they are. In reality, even those constants are all in a position favorable to life (arbitrarily -- a great mystery to the secular materialist), and the likelihood of that happening by chance is more unlikely than a planet such as Earth forming on its own. And then we get to abiogenesis, which requires an equally long series of unlikely events to have happened.
So the question is, what is more believable? We have an intricate series of physical laws and constants (arbitrarily established, to the best of our understanding), a wildly improbable set of coincidences to establish a planet such as Earth, and even after Earth is established a fantastically unlikely set of circumstances to generate life. Is it more likely that God established this? Or is it more likely that it was chance? Keep in mind, the universe has an age and limits, so it isn't just a matter of enough time and enough space. In fact, to put things in perspective, the odds on the universe having a planet such as Earth form at any point in its existence is approximately the same as the odds of winning at roulette. 53 times in a row. Then winning another 49 times in a row for abiogenesis. Then another 180 times in a row for the fundamental physical constants.
Hey, maybe the atheist feels lucky and should go to Vegas. But given the choice between a universe where the dice were rolled at the very beginning and somehow we managed to luck into the most improbable situation that defies comprehension, or a universe established by God for the creation of life, I know which one seems more likely to me.