The problem isn't really about using it yourself, it's that people don't need to ask your permission to use it, therefore you can't (easily) profit from it. Possibly quite annoying if you're in the AI business.
You don’t own the copyright for any picture generated by a computer, whether random or intentional
That said, chicken can't own copyright, and they are the author, therefore no one owns the copyright.
The law generally won’t help you narrow down where the exact line is between those two, as that’s up to the courts to decide on a case-by-case basis.
It’s when then computer creates the art itself that it becomes the artist