Chickens are less likely to suffer from depression than to show signs of sickness or pain. A sick chicken is lethargic, standing mainly in one spot, maybe nodding off. A chicken in pain will do the above and hold their tail low and flat.
However, trying to diagnose a sick chicken is a real exercise in mystery solving. You need to gather as many clues as possible, starting with what has this hen been doing and eating in the past few days. Is it very hot where you are? Have you sprayed for insects lately? Has she been around machinery that leak fluids onto the soil? How about a compost pile? If so, what has been going into it? Is it overly wet? Has she been laying regularly and stopped all of a sudden?
Her poop may tell you something, too. Is it white and watery? Or thin, watery, with greenish bits in it? Is there blood in it? Do you see any worms?
Have you examined the feed for mold? Have you examined the chicken and coop for parasites?