When cooked chicken has gone bad the cooked chicken will turn to a different color.
The bad cooked chicken will turn green-gray or gray in color as it spoils and the more of that color it takes on the more spoiled the cooked chicken is.
The cooked chicken that has gone bad may also have a bad smell or bad taste to it as well.
A few other signs that your cooked chicken has gone bad is the cooked chicken has a bad smell, a slimy or slippery texture and mold growing on the chicken.
Cooked Chicken should last between 4 to 7 days in the refrigerator without going bad but it loses it's freshness.
If you have raw chicken then it will only last a couple days in the refrigerator and will be begin smelling bad as well and get slimy.
If in doubt throw the bad chicken out because it's not worth getting sick over it.