What causes a horses chest to swell?

There could be several reasons why a horse has edema, which is a swollen, fluid filled area. An insect bite or sting can cause this kind of reaction. Another possibility would be some kind of trama. If the horse displays no other symptoms like lethargy, refusal to eat, then keep an eye on the swelling. It might help to apply cold compresses and it may give him some comfort. It the edema worsens or the horse exhibits other symptoms, as mentioned above, call your vet and get his advice.