How to completely remove an issue from GitHub?

Is it possible to completely remove an issue from the GitHub issue tracker?

No, the github API only allows you to open/close/reopen issues. Here's the Issues API docs.

You can edit an existing issue (let's say if it's a duplicate) and you can change the title, description and target milestone to be something completely different. That's as close as you can get to removing the ticket, AFIK.

Update Nov 2018: You now can delete issues if you are a owner of the repository!
See "Github - remove issues entered in error"

https://docs.github.com/en/github/managing-your-work-on-github/deleting-an-issue mentions:

People with admin permissions in a repository can permanently delete an issue from a repository.

For other people (without permission), questionto42's comment shows that you can ask to GitHub support for the issue to be deleted, as illustrated here.

At May 2018, original answer:

Three 8 years later, and closing issues remains the answer (still no deletion possible).
See "The Ghost of Issues Past", where GitHub advise to check and close:

• issues opened over a year ago state:open created:<2013-01-01
• the ones I'm involved with involves:twp state:open created:<2013-01-01
• and those not updated in the last year involves:twp state:open updated:<2013-01-01