Stress is an emotional state, right? Chickens get stressed, you can't deny that. So why couldn't they feel another type of emotion?
I haven't lost a chicken (yet), so I've never observed mourning in them, but I've observed excitement (get a bag of treats out), contentment (when the sun comes out and warms the soil), worry (where did everyone go?), panic, stress, pain, fear, playfulness... These are all things chickens feel and act upon.
If you have never seen a horse pace up and down a fence for week, calling for it's weaned foal, refusing to eat, or heard the mournful cry of a cow separated from its calf, or even seen a fish (yes, a fish) perish from depression, then it may be hard to believe. But for those that live it, it is very real.
I know a lot of people don't think much of vets, but they have undergone years of study, of which animal behaviour. Ask your vet what he/she thinks. Or buy a book on degus... a small rodent from South America. It is recommended to keep more than one degu, because otherwise they can get depressed and let themselves die.
All of that to say: yes, I believe chickens can mourn. If a fish can, then why couldn't a chicken?!