Add gelatin to soup as a replacement for stock? My wife made some chicken soup last night, but we didn't have any stock to start it with, so we used water.
Flavor-wise, the soup was fine - it was just lacking the mouth-feel associated with good soup.  There was plenty of oil floating on top of the soup, so it wasn't lacking in fat.
I was thinking it was probably because we'd started with water instead of stock.

We're planning on making our own stock soon (so many good tips here!) but we didn't have any on hand last night, nor were we prepared to run to the grocery store.
However, we realized after we'd eaten the soup that we had a couple of packets of powdered gelatin in the cupboard.

Would powdered gelatin have given the same mouth feel as stock?
I'm looking for the online reference, but I remember reading in Cook's Illustrated that they were able to substitute a bit of gelatin to mimic the mouth-feel of homemade stock. I did find a beef stew recipe that used gelatin. 

Based on how you described your recipe, I would say that the long cooking of chicken bones is indeed what's missing. You might get a better result if you roast your chicken breasts and vegetables before cooking them in the broth.