Yes sadly chicken wire is not predator proof.
The joins are only twisted so it also means that as well as it being possible for animals to bite through it, once a wire is broken it can unravel too. We don't rehome to people to use chicken wire for this reason.
This isn't just hearsay either; I have one rabbit here who's sister was taken out of her hutch by a fox who'd chewed a hole (with chicken wire for mesh) and also was involved with another rabbit who was found in a hutch that had been dumped in some scrub ground. The front of the hutch had been ripped open and half a rabbit was found stuck in it. Luckily the passers by who first spotted it took a closer look and found the remaining rabbit still in the hutch. That rabbit made it into the rescue that I used to work for some years ago. Much scarred by the experience too.
I also recently had a run donated, it was unuseable - it had holes in the chicken wire, that had been patched up - so am guessing that either a predator or one of the rabbits themselves had managed to bite through.
I buy my weld mesh from Wickes, although you can buy different gauges from various suppliers. There are different strengths but most are pretty good. The benefit being that each and every joint is as its name suggest - welded together so even if one strand breaks you don't get a large hole developing.