In the coin toss scene, what does Chigurh have to say about fate and chance? What does the coin toss symbolize?
It's one of my favorite scenes in the movie, and it reads well in the book also. The idea he presents is a powerful one, in that this coin he has in his pocket had traveled for twelve years to get to this one place, at this one time, in a gas station in the middle of the Texas desert. This same coin, then is to be used to determine a man's fate, even though he is not fully aware of it. Imagine the number of transactions and the incredible random timing and coincidence of this coin being in Chigurh's hands at this particular point. I think the idea intrigues Chigurh too. He is a man who believes everything happens for a reason, that fate plays a role in these decisions, if not the dominant role.
Also for Chigurh, this is perhaps how he has come to rationalize the murders he carries out, that these victims were fated to die at his hands, and that he is merely the delivery mode for random chance. We also see this in the man Chigurh pulls over by the side of the road, just a random car with a random person that happened to be the next car in front of him.
Overall, the coin toss can symbolize the randomness of life and death many humans face at one point or another in their lives. Those killed in war and those not, those who live through the Holocaust only to be killed by a mugger fifty years later, or those killed in an accident that was someone else's fault (accident scene with Chigurh towards the end of the story too). All of these are events beyond our control, random fates determined by chance. Chigurh believes in this randomness, represented by the coin, very deeply. He believes it absolves him of all his crimes.