Symbolism, Imagery, Allegory
Head(less) or Tails?
Chigurh carries around a coin like he's Two-Face from Batman, except Chigurh only has one face—the face of evil.
Chigurh really has an affinity for coin tosses. Some are seemingly random, and some are planned—though isn't a coin toss the essence of randomness? Basically what Chigurh likes to do is make people call heads or tails, and then if they've called wrong, he shoots them.
He pulls the ol' coin-toss trick on an unsuspecting cashier at a gas station, for example, making him call the coin, while heavily implying that if he calls wrong, it'll be the last call he ever makes. "What's the most you ever saw lost on a coin toss?" (2.4.58) he asks. The answer? Your life.
Chigurh casts the coin toss a weird mix of luck and fate. Just by nature of it being a coin toss, some luck is involved, but Chigurh acts like the ultimate outcome is fate. "You've been putting it up your whole life. You just didnt know it" (2.4.74).
Luckily, the old man calls the coin correctly. The grand prize: the coin. Wow. A whole twenty-five cents. Don't spend it all in one place, dude. As Chigurh tells him, "Dont put it in your pocket. You wont know which one it is" (2.4.95). Which is a lie, because Chigurh already told him the coin is from 1958. It's the one with 1958 on it.
Carla Jean isn't as lucky. She calls the coin wrong, and Chigurh kills her. But he had already promised that he would kill her if Llewelyn didn't give back the money, so is it fate that Carla Jean called the coin wrong? Would Chigurh have not shot her if she called it right? Would she ever have been able to call it right? Our heads hurt just thinking about it.
Carla Jean complicates things by telling Chigurh she didn't do anything to deserve this. He agrees with her, saying "You didnt do anything. It was bad luck" (9.2.119). But later he says, "The shape of your path was visible from the beginning" (9.2.143). So which is it, buddy? Is it fate, or is it luck? We just don't know anymore.
But Carla Jean makes another point that Chigurh really can't duck out of: "You make it like it was the coin. But you're the one" (9.2.134). She's right: Chigurh is the one who shoots her in the face, not George Washington. This echoes something Chigurh said to the convenience store clerk: "It's just a coin. For instance. Nothing special there. What could that be an instrument of? You see the problem. To separate the act from the thing" (2.4.97).
Carla Jean's point, though, is that in a way, Chigurh is trying to make it so he's not really responsible for the crimes he commits. Is this actually something he tells himself in order to make himself feel better? It's unclear. If it is, then maybe there's some humanity to him, after all. We really can't be sure.
It's also possible that these coin tosses symbolize the fact that the drug trade is so huge, so powerful, and so evil that everyone involved in it—and everyone who accidentally gets in the way of it—is either just an instrument or a victim. Just as there's no escape from fate, there's no escape from the evil unleashed by the drug trade.