As part of a migration the Joind.in project made to track their bugs on a hosted Jira instance instead of the Issue Tracker on Github, Lorna Mitchell, one of the leads on the project has written up an import script she used to move current issues. The code is in her latest post.

I migrated only our open issues, and comments (and the comments ended up a bit weirdly formatted on the other end but this was the best they could do). It was nothing pretty or clever but in case it's useful to someone else.

The script connects to the github API and pulls down the information for the open issues including their titles, user and body of the issue. This is then used to make another connection for each to fetch their comments. The whole thing is dumped out to a CSV file that can be easily imported by the Jira team.