Run, Run, Chicken Run, sung by The Serendipity Singers on their We Belong Together album (1966?), attributed to Galbraith/Teifer/Marens, (possibly related to the Link Wray instrumental which Severn mentioned?)

An Peata Circe (The Pet Hen)

For just a mention of chickens:
Sourwood Mountain
It Ain't Gonna Rain No More
Egg-suckin' Dog