You might want to click on over to the side there and make sure you've read our thoughts on the symbol of the money, because we're about to say something really similar here: the coin might symbolize randomness … or it might symbolize the way we desperate want to assign symbolic meaning.
Think about this: in two different scenes, Anton Chigurh flips a coin to determine whether he's going to kill the person he's talking to. To him, the coin represents the randomness and risk of every single moment of human life. When the gas station clerk asks him what he's risking in calling the coin toss, Chigurh answers, "You've been putting it up your entire life. You just didn't know it."
But just when we think the coin symbolizes randomness, Chigurh turns around and suggests that the coin has some sort of predetermined fate attached to it: "You know the date on this coin? […] 1958. It's been travelling 22 years to get here. And now it's here and it's either heads or tails."
So is it fate or chance? Did bad luck bring Moss to that botched drug deal, or was he pulled there by some deeper force he couldn't even recognize? Is Chigurh compelled by forces he can't control, or is he just pushing responsibility off onto something (anything) else?
By the end of the movie, it's almost impossible for us to tell whether the coin symbolizes a deeper meaning or no meaning at all. Chigurh sums up this paradox when he says to the clerk, "Don't put it in your pocket […] It'll get mixed in with the others and become just a coin. Which it is."
So on the one hand, the coin means everything. On the other hand, it means nothing. When Carla Jean Moss insists that "The coin don't have no say" and tells Chigurh to take responsibility for his killing, Chigurh can only respond, "Well I got here the same way the coin did." In the end, maybe the coin symbolizes the way human existence walks a knife's edge balance between fate and randomness.
And then again, maybe it doesn't.