But it would be labelled as chicken coming from the US, this makes it easy enough to avoid!?

Already today, I always read on the label to find out from what country the meat I'm about to buy comes, I always prefer local over imported as I think it is something little I can do to reduce unnecessary emissions and would hence anyway not buy meat that comes from another continent, just to get it few cents cheaper

It is however often not possible when eating meat at restaurant for example :(

Things that aren’t labelled properly are illegal in a lot of European countries an the EU doesn’t have power to overrule that. GMO products has pushed this hard over the years because almost no one wants to buy them.

Hell in Denmark where I live, half of our super market chains outright refuse to carry things like eggs from cage-hens. So they likely wouldn’t ever offer chemical washed chicken American for sale, and they’ll likely even use it in commercial to tell consumers how much better than their competitors they are.

Interesting that so much of the activity of "free market" advocates is centered around reducing access to information.