Isn't this the aviary between the Red Pandas and the now-vacated bongo (ex-wapiti) paddock?
If so it's had Grus japonensis in there for well over a decade, so 'crane aviary' would seem perfectly appropriate. I don't remember peafowl in here, but I have never seen storks in there either.
There are two pools and the netting still seems to be in place, so those pigs could paddle and fly as well
The building and foundations look interesting, so I'm guessing they will be more off-show aviaries.
It's "Peacock Aviary" (oddly, not peafowl) on all the maps from my early zoo visits. There were all sorts of things in here when I was a child, mostly flightless (or flight restricted) because as Rob says, the roof is a relatively recent addition.
The small stone plinth has been within the aviary for as long as I can remember. I don't know its history, but it seems to be remaining in place - although now I've typed this someone is probably taking a sledgehammer to it.
With this and 'Islands' its good to see Chester is still living up to its old motto of 'Always Building'. Do they still promote that anywhere nowadays?