How do I delete an extension in my Chrome developer dashboard?

The new beta dashboard has an archive option. (more -> archive)

You can't delete an extension from the Chrome developer dashboard.

In the past, there was a delete button at the dashboard, but it has been removed because developers accidentally removed apps/extensions (and then tried to re-upload the app/extension with the same ID, which failed).

Unpublished extensions/apps do not count toward the extension limit, so there are no consequences for having a lot of unpublished apps/extensions besides the clutter at the dashboard.

If you're really bothered by the entry at your dashboard, create a user style, user script or extension to hide it.