Chicken meat that is starting to go bad will take on a gray color and a dull appearance. You also want to make sure your chicken isn't damaged, seems deflated, or bruised.
In terms of texture, if you poke the meat and it either stays poked or feels solid, don't buy it. You want the meat to have a little give but also bounce back to where it was.
If liquid pools in the container, that's a bad sign, too. The excess liquid comes from the chicken absorbing water while it is chilled and can make the meat mushy and bland.