Hi, getting a chicken to live a long life I think is a mix of many things. Some things you can control and some things you can't.
I currently have a flock "according to chicken math" of about 50. Some of my oldest girls are 9 years old. They are Buff Orphingtons and part of my original flock I started almost 10 years ago. I currently have 5 remaining from that original starter order.
I can say that one of the keys to a chicken living a healthy life is nutrition. I don't feed my girls many treats, doing so dilutes the nutrition that they need to be getting from their feed. A good chicken feed like Purina is a complete balanced scientifically engineered feed for poultry.
Next, I would have to say a secure free range space. I free range my flock every day unless we are expecting bad weather. I have a large backyard that is fenced in with a 8ft wood privacy fence. I have had chickens for almost 10 years and have never lost a bird to a predator. I usually loose them to old age or illness. Here is a pic of my chicken yard.
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Something else I do is put vitamins and electrolytes in their water daily. One or twice a week I will add some probiotics that you can find at a local feed store for poultry. This ensures that in addition to the feed they get a complete balanced diet every day.
I also do not use any chemicals in my backyard, their free ranging space. For example, I have my gardens planted in my backyard but use nothing for the bugs on my plants. I leave that to the girls.
Keeping on top to worming, mites, and lice is also a must. I don't worm my flock all the time only when they need it or I suspect worms are a problem.
Make sure that they have a clean and dry place to call home. Keep on top of coop cleaning and make sure that in the winter or rainy seasons that their digs are clean and dry. This little stop goes a long way.
I hope that this helps some. I consider my self very lucky to have 5 girls that are over 9 year old. From what I hear that is old for a chicken and an indication that I may be doing something right.
Best of luck to you and your flock.