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
You don’t own the copyright for any picture generated by a computer, whether random or intentional