In native English we would simply say you choose chicken or you choose the chicken (if it was a specific menu item). You would never hear someone ordering a meal ask for poultry. Poultry is more a farming term or maybe a restaurant wholesale ordering term.
Chicken means both the animal and the meat from the animal (and a coward). However, pork is pig meat and beef is cow meat, venison is deer meat and mutton is sheep meat. Often in English, the word for the meat of an animal is NOT the same as the animal itself, to protect our delicate sensibilities from the harsh reality of butchery.
The exceptions are all the birds: chicken. duck, goose, pigeon, pheasant, quail and, in addition, goat, lamb and rabbit which is hard to understand given lambs and rabbits are cute.
I can't imagine a native speaker ever saying "you choose poultry" though. Then again, unlikely sentences are not uncommon here. When referring to meat, it generally refers to the entire class of meat, not specific instances. So you'd be more likely to hear, "I avoid poultry" than "pass the poultry".
On a separate note, you have the most impressive duolingo profile I've ever seen! Wow! Absolutely amazing, and inspirational. :)