Change effective on 13 April 2016
Org members can now create apps in Private Spaces, whereas previously this was limited to org admins. With this new feature, org members can do this if they are explicitly given the permission by an org admin in the Access tab for a space. (This is an editable permission on the space level, rather than the org or app level.)
The feature helps further strengthen security for Private Spaces by helping reduce the necessary number of org admins for each space.
See the Dev Center article for more details.