Just in case you missed it, there is a prototype for a Mylyn and Github connector available. Please see https://github.com/blog/852-github-mylyn-connector-for-eclipse for the official announcement.
Installing the connector is pretty straight forward you can directly install it from the Eclipse Marketplace client. The only pre-requisite is that you add the Orbit repository http://download.eclipse.org/tools/orbit/downloads/drops/S20110422041657/repository/ and install “Gson” from the com.google.* category (thanks to Christian Trutz for the tip on twitter).
Importing your issues is as easy as File -> Import -> Tasks -> Github Task Repositories and then you can define new queries for this repository.
The first test unfortunately failed. During a submit of a new issue with the error “Submit failed: Unexpected error: Unprocessable Entry”.
Still the connector looks very promissing. Git is my favorite version control system and I love Github. Its great that soon Mylyn will also to share issues and ther context via GitHub.
I suggest you give it a test run. If you find issues you can report them in bugzilla: Mylyn EGit Connector.
Update: The bug is already fixed, looks like testing will get your bugs solved fast.