Could you send a link to it so we know what we are talking about? I get different products when I Google “deer fencing”. None of them looked very suitable, by the way.
Chicken wire is basically meant to keep chickens in. Many predators like dogs, coyotes, and big raccoons can tear chicken wire, either pulling it hard enough to untwist the connections or literally breaking it. There have been photos on here of that destruction, usually by big dogs, but those photos are pretty rare. Chicken wire will provide protection against many smaller predators, skunks, possum, smaller raccoons, most birds of prey, probably a fox. Many people on here describe a chicken wire run as worthless. It’s not worthless, it does provide a fair amount of protection. But they are still vulnerable to larger predators.
The basic question is how easily could you cut or tear that deer fencing if you had sharp teeth or claws and what is your risk tolerance.