Have you ever cross on the land border into Mexico? I have cross thousands of times, every day, sometimes many times a day for years.
There is no one there to ask if you are bringing anything, a random red light turns on and you go to a search area, people get send back to the US sometimes if they don't let you cross something. But you will go to jail if they find a gun or very large quantity of anything, like 200 cases of chicken, 1000 tv's, etc..
Yes, like once a month there are also inspectors on the US side checking on cars before you reach Mexico. Chickens are not illegals, just tell them you will make a u-turn back to the US.
I am just making a suggestion, you will do what you are comfortable of doing. Now coming back to the US, don't bring anything.