Why do some recipes call for sugar in a brine? In making a brine for my chicken, I came across a lot of recipes that call for sugar in the brine.  I understand the general idea behind brining, but don't understand what benefit the sugar provides.  

In this answer, @papin links to a PDF that states the following (emphasis mine):


  The law of diffusion states that the salt and sugar will naturally flow from the area of greater concentration (the brine) to lesser concentration (the cells). There is also a greater concentration of water, so to speak, outside of the turkey than inside. Here, too, the water will naturally flow from the area of greater concentration (the brine) to lesser concentration (the cells). When water moves in this fashion, the process is called osmosis. Once inside the cells, the salt and, to a lesser extent, the sugar cause the cell proteins to unravel, or denature. As the individual proteins unravel, they become more likely to interact with one another. This interaction results in the formation of a sticky matrix that captures and holds moisture.


This makes it sound like sugar isn't really an important part of the osmosis process.

Is there a chemical/molecular reason to add the sugar, or is it just to add some flavor to the chicken breast?
The sugar is simply used for flavoring; the fact that it helps brine to a lesser extent is just an added bonus. The sugar also aids in browning via the Maillard reaction, though this can also result in burning in a high heat application.

I suggest brining two boneless skinless chicken breasts -- one in a salt-only brine and the other with the salt &amp; sugar brine suggested by Cook's Illustrated. You should notice a difference in both flavor and appearance.