If you are in the Coop or the Barn, I think you can only obtain as many Hay in your inventory from the chest as there are animals in the Coop or Barn. And then you can put that Hay in the tray/trough for the animals. You may be able to put the single Hay from your inventory into a regular Box/Chest you crafted and then go back to the one in the Coop or Barn to retrieve another Hay, but I'm not sure if this works. I don't have a save I can test this in right now.
My guess is you currently have one Chicken in your Coop? If this is the case, then I believe this Hay mechanic in the game is working as intended.