Welcome to Permies, Vanessa! Congrats on the new property. That is quite the vine. It does look an awful lot like wild grape, though I agree with Carla to be 100% sure on your ID.
If it is grape, you're right that it's a great resource for
chickens. Mine adore wild grapes and the leaves. So it's wise of you to consider other options besides chopping. I don't have great answers, as I am trying to learn to work with similarly huge grape vines on my land. One thing I do know is that pruning ones that size at this point in the year doesn't usually go well for them. When I have had to do that, they bleed for a long, long time and get crazy fungus growing on the cut ends. I've also found that once they reach that size, they're often not super flexible and options for redirecting them are somewhat limited. I've sometimes been able to use rope to tie them out of the way until a better time to prune though. I'd be inclined to do something like that, if possible.
Hopefully someone else has better answers for you about if there is a way to prune and train them over time.
“Action on behalf of life transforms. Because the relationship between self and the world is reciprocal, it is not a question of first getting enlightened or saved and then acting. As we work to heal the earth, the earth heals us.” ~ Robin Wall Kimmerer