In your particular situation where, if the dog gets loose it apparently has access to the chickens at times, I would re-home the dog. If you can arrange things so the chickens have a safe, dog proof coop/run and the dog has it's own run as well then you can make it work.
Lab's are high energy, active dogs who don't lend well to sitting around in a pen or kennel all day unless they are given several intense exercise periods during the day. You may well end up with a dog with nasty habits like digging out or sitting around barking it's head off all day and night.
I have kept both dogs and chicken's for bazillion's of years and they just don't have access to each other, ever. And I've never lost a chicken to a dog. It's easy to do with the benefit of everybody gets to keep their home and family member's don't become at odd's with each other.
Good luck! Hope you find a solution that works for you. I love my dogs and dogs in general but they sure can be a pain in the butt!