Find some Special Chicken Feed and return to your befriended chicken. When you find it, /cheer at it before trying to give it the Special Chicken Feed. This quest starts and ends in Shattrath City, Duskwood, Elwynn Forest, Northern Barrens, Westfall, Redridge Mountains, Tirisfal Glades, Howling Fjord and Azuremyst Isle.
Here you can buy CLUCK! Quest Boost for EU or US Servers.
You'll get guide for completing CLUCK! Quest Boost