They can coexist in a large area, at least. Other than the yardspace, I was actually in a very similar situation.
When I was... sixteen? My brother came home one day with a two-year-old beagle gyp. She was pretty nervous around new people, so after socialising with her a bit, we tied her out in the yard. Didn't even think of the free-ranging chickens.
Well, about an hour or so later, I heard a commotion, so I raced outside, and she had my rooster in her mouth. A few seconds later, she no longer had Chester in her mouth, and she hasn't looked sideways at a chicken since. 
That would not have been my chosen way to do that, and a beagle would never be my first choice to have around chickens. But it did work out just fine, and has for several years (my brother went and joined the military, so his dog is still living with my parents' chickens, and probably will be until she dies), so obviously, it can be done. 
Now, my parents have a significantly larger property than a small backyard, so boredom is probably a factor you should consider. Thus, I would find a breed that is easily trained, and not easily bored. Beagles are not easily trained.