I always have at least 1 hive in my small fenced back yard and have 3-4 chickens. Hive is not right next to coop, but when I used a chicken tractor (mobile coop) I often put it very near the hive.
My chickens are often in the vicinity of the of the hive, scratching around for bugs/grubs but they never hang out right in front of it. They never seem to eat live bees or even dead bees. I have dumped enough dead bees around and always figured they would eat up the dead bees but they never do.
My chickens love to hang out on my deck :'(, and I have an indoor observation hive that has an outlet on 2nd floor above the deck. So, there are always dead bees on my deck. Chickens never touch them (wish they would clean them up, instead they just poop on my deck and make it a further mess :'().
The chickens never seem to jump up on the hive, but my regular backyard hive has a "garden cover", so it is an angled copper roof and maybe that is why it doesn't appeal to them - they seem to jump on everything else.
If I lay a frame of brood with exposed larvae in front of them . . . . . well that is a different story. :shock: They LOVE to eat the larvae out of cells. If I scrape some drone brood off a frame and larvae are exposed . . . . they will grab it and try to get at all the exposed larvae. They haven't seemed to figure out capped brood though, they will only eat the larvae from cells where they can easily see the larvae. But, the larvae are evidently like lays potato chips . . . they can't eat just one!
And for some humor to the chicken / bees combo. My wife and I were trying to take a timer photo of us next to our backyard bee hive this past summer for national honey bee day. We got photo bombed by a couple of our curious chickens who were inordinately interested in the camera sitting on a chair.
Clickable image below takes you to the rather hilarious full sized version. They were not photo-shopped in. They just snuck up to the camera while the timer was winding down to shoot the pic. I took about 3 pics and each time Gypsy went up to the camera after I ran towards the hive and looked cockeyed (hen eyed?) into the camera. I actually didn't know they got into the pictures until I checked them later.