Fruit or nut or edibles which birds don't eat?

[mountaindweller]

In our chicken run we have a poor drainage (but I can build mounds) and it is pretty big, I would like to plant some trees as well for providing shade. The sheep is there at night too (and she loves pruning trees). I would like to plant something there which grows fast (that I can remove the fence early), and might have an edible crop too. Chestnuts grow well here but the cockatoos get each and every one. Any ideas? they should survive heavily fertilized environments.
We are in the mountains, and in winter nights it gets below freezing -5°C.
I have an olive tree there, it does not really grow fast and a Japanese raisin tree, which likes it there.

[raymondo]

The problem is that anything humans like to eat birds often do too. There's a new small walnut cultivar called Chandler. It's small enough to net against birds. There are also small almonds which could be similarly netted. Not sure how either would cope with life in a chook pen but they can certainly handle the cold, down to -10°C or so.

[cletus]

According to Edible Landscaping, the birds will leave alone the che fruit, a fast growing mulberry relative. Mine was going to fruit this year before a derecho storm broke my tree so I can't say from experience.

[castanea]

Birds never bother my che fruit, nor do insects or anything else. The problem is that most humans won't eat it either. Tough tree though and very pretty unless you have thorns.