without knowing why the dog does this I can cautiously give some pointers but I would like to hear more, like what's the dogs typical day like, is he an excited dog, does he have lots of endurance?
Also I'd like to point out there could be more than a few causes, like boredom, frustration, teeth problems, diet problems, or maybe he just learned it was a fun behavior.
If heard some good suggestions, I like the chicken wire idea, but I've known determined dogs to chew even through that. I've used the pepper spray (boiled cayenne pepper in water) which seems to be pretty good, but as someone pointed out some dogs end up liking it. So anyways here are my pointers.
1- make sure the dog has enough "controlled walks" meaning the handler is the one in charge, dog does not pull ahead or stop whenever he wants.
2- make sure he knows you don't like it, take a day and just watch and wait for him to try, and block his way to the tree and tell him "no", no matter how many times he tries each time block him by standing between him and the tree. At least he'll know you don't like it.
3- make sure there are safe alternatives, balls, toys, maybe even sticks of wood he is allowed to chew on.
4- I'm not sure how energetic the dog is but sometimes labs can be in need of some sort of regularly occuring high intensive exercise, high speed ball/frisbee fetching, running alongside a bike, swimming, or even a treadmill can do some good.
note the fifth is a last resort
5- I do not know anything about dog nutrition but if you've tried everything else and he keeps on doing it I would expirement with different dog food brands or vitamin supplements with the help of your vet of course.
If you describe to me more about your dog I may be able to figure out some more, I've been training dogs for 10 years and studying dog behavior for 6 years and am trying to get more experience in solving behavior problems. Tell me what the dog does every day, what the family does with the dog, his personality, and when you find him chewing, is he relaxed lying down while chewing, or is he excitedly tugging and ripping, does he shake the pieces or just chew his pieces smaller and smaller? Also tell me anything else you may think I'd want to know. Anyways I'm here to help if you want.