And you have to apply for it :P Wow, what a way to be welcoming to newcomers:
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+button in the bottom left, pick your org from GitHub etc...
can you try add Gitter Private Repo Access to your own, wait a few minutes, refresh, then see if BuildGem appears on the Add a room dropdown?
you should be able to add this scope under the Add a room modal, there should be a link to turn on access for private repos.
alternatively, remove it from the oAuth Application Policy page, as above - wait a few mins, refresh and try again