This is further into the undeveloped portion of the park, so
trails are intermittent at best. If it hasn't rained recently, you
can just walk along the creek. If it has rained recently, you may
need to cross back and forth across the creek a few times to find a
decent path. It would probably be best to stay away during or after
heavy rains.
If you would like, you can add a few answers of your own as to
why that chicken actually DID cross that road.