Battlechat have posted a neat, short, and easy video on how to obtain the pet chicken from Westfall. If you're questing in the area, you really should pick it up. I completely forgot about it, and I'm so glad I found the video, especially now that I have a new feathered friend. 

• Head to Westfall and talk to farmer Saldean. 
• Buy Special Chicken Feed.
• Select a chicken and type /chicken.
• Repeat the /chicken command over and over, until it turns from yellow to green.
• The chicken will suddenly gain a "?" marker, at which point you can complete the quest for your new friend. 

Thanks, battlechat!