I know there some that claim it happens naturally, but that is a flat out lie of gargantuan proportions.
Or not. Mike, there is no lie.
Earth's oceans are approximately 1.3x10^21 liters. Each liter is 3.34x10^25 molecules of water, or 4.34x10^46 molecules of water in the oceans. For the sake of argument, let's say that is how much water was present in primordial days. During the time when the oceans were turbulent with storms, water was stirring around constantly, and anything dissolved in it would be stirred around as well. Let's say that the concentration of that witch's brew back then was about like it is now, with 3.5% salt. According to Richard Feynman, at 20 degr. C a water molecule encounters on the order of 10^14 collisions per second. Each collision is 1 opportunity for the colliding molecules to do something constructive.
Each billion years is 3.154x10^16 seconds. In 1 billion years, you would have 4.34x10^46 x 0.035 x 10^14 x 3.154x10^16 collisions = 4.79x10^75 collisions. Nature would have at least that long if not twice that (i.e. 2 billion years) to iterate over possible collisions that led to formation of useful chemicals.
Let's say that the odds are 1 in a trillion that a collision between two molecules would lead
towards life, and that you needed a trillion such collisions to actually
start life. A trillion is 10^12. So that's a trillion collisions to go forward and a trillion forward steps required. So with those numbers, you STILL have 4.8x10^51 iterations. Want to change the odds to 1 in 1 quadrillion? That's 10^15, but you still have 4.8x10^45 opportunities within those odds.
Now, let's take into account that the concentration of those interesting precursors to life was probably no more than a part per million(10^6). Which means you still have 4.8x10^39 constructive collisions. That number in USA terms is 4.8 duodecillion. (Note that the UK uses different nomenclature for numbers that high.)
Nature iterates on her solutions by sloshing around the oceans with storms, by dissolving useful minerals, and then the Miller Urey experiment shows that those building blocks could really have been there. The odds suggest it not only COULD have happened, but was actually LIKELY to happen. And note that I didn't say "start HUMAN life"... just start life and watch where it goes.