Eating chicken that has been cooked and properly refrigerated or frozen is okay to eat past it's use by date as long as it doesn't have a bad smell to it or doesn't look bad.
I've kept cooked chicken in my refrigerator for 3 to 7 days and have eaten it without any health issues because it was still good and didn't smell bad.
The use by date is just a general guideline and food establishments have to follow that rule for safety reasons but at home you can still eat the cooked chicken or past it's use by date.
You can keep the cooked chicken longer than a few days in the freezer which will make it last longer.
If you keep the cooked chicken in the freezer it can last for 6 months to a year and still be good to eat.