A little insight from a member in Kentucky. Depending on the part of Kentucky the OP is in,there may be no "animal control" officer. Many of our counties have that problem. Even if there is an animal control officer most of them will not chase down or catch animals,you have to do that and THEN call them to take the animal away.
Also,in Kentucky animal control may only take dogs and maybe cats. Many animal control offices in Kentucky are like that. No livestock,no wild critters, no exotic pets, nothing else, just dogs/cats.
Another problem....While we are not all barefoot,tobacco chewing,bib overall wearing heathen that the media portrays Kentuckians,there are still many that seem to live that way,resulting in dogs,chickens,goats and all manner of critters roaming freely around neighborhoods and the so-called owners will fight over their "right" to allow that to happen.
Keeping this in mind I can understand the OPs question if they are new to the state or have recently move into a rural area.
While I hate to see these chickens killed needlessly, that may be the only recourse the OP has. In that case,leave the shotgun in the house,grab a .22 rifle and using a head shot dispatch the chickens quickly and mercifully. A shotgun WILL NOT do the job properly!
