I just re-watched No Country for Old Men, and while it is implied that Chigurh is hired to find the money and kill whoever stole it, it is unclear who hired him. He kills the two men in the beginning who are with him at the site of the gunfight and who give him the transponder, why would he kill the men who presumably work for whoever hired him? Then he kills the man in the office building, after confirming that that man gave a transponder to the Mexicans as well as him, implying that he had something to do with hiring Chigurh. Finally, when I was reading about the book that inspired the movie, it mentions that Chigurh returns the money towards the end.. who does he return it to? It seems he has killed the people that hired him.
Edit: after the first answer, I guess I should elaborate.. It seems that Chigurh worked for the white men who were buying drugs from the Mexicans (they would have had access to the transponder, as it was their money), but my real question is, if Chigurh worked for them, why did he kill most of them? It is pretty clear he has a sense of (perverted) honor and loyalty, so killing the people who hired him seems to go against everything he is about.