Actually, left to their own devices I doubt that many even make 2 years of age. Most get et by something
The answer totally, totally depends on what you mean.
"What is the longest that chickens sometimes live?" 15-25 years. But virtually none ever make it to that age, for a whole variety of reasons not entirely limited to those related to getting et. Expecting a chicken of yours to reach age 15 is like expecting your gramma to reach age 110 -- it does happen, but not on a regular basis and it's not something to *plan* for.
"What is a good ripe old age for a well cared for captive chicken?" If you're getting many of your chickens to 6-10 on a regular basis, you're doing pretty well.
"What life expectancy can a well cared for captive chicken expect when it's born, assuming nothing eats it?" Depends on breed and what diseases are floating around in what abundance. High-performance layers like sexlinks seem to have a distressingly nontrivial prevalence of deaths due to various female troubles, starting at 18 months or so (ish) and many succumbing in the next few years. Some other breeds, mostly ones that lay less to begin with, seem to have less likelihood of fatal reproductive problems and thus have less taken off their lifespan from those causes, on average. Also chickens in a situation with many new diseases being introduced, or with fairly stern strains of multiple chronic diseases resident in the flock, will not live as long on average. So there are a lot of factors that affect how long an individual person's chickens are likely to survive.
Pat