This is the official GDG logo. You are free to take and modify it (per the customization guidelines listed below) for your own chapter's logo.
The high resolution source vector graphics in Adobe Illustrator format are attached below. If you already have the OpenSans font, you can download just the GDG-Logo.ai file. If you want it bundled with the Open Sans font used for the text in the logo, then download the ZIP archive that contains both the GDG-Logo.ai file and a folder with all the variants of the Open Sans font you should need.
GDG Program Icon
Chapter Logo Customization Guidelines
GDG Logo Generator
It still has a few rough edges, but, it does generate SVG files. You will have to load the resulting SVG file into some other application and then export to PNG. Inkscape is a free application available for common platforms that will do this for you. See http://inkscape.org/download/
In terms of rough edges, it doesn't seem to work for me in Chrome on Goobuntu (variant of Ubuntu used internally at Google). However, it works as advertised for me on the Mac and even on Goobuntu using Firefox. Depending on the browser involved, you will either get a text link dynamically added below the image that you can click on to download your custom logo as an SVG file *or* the application may load the SVG file into separate browser tab. Either way, you should be able to save the SVG file and then use Inkscape or other vector graphics app to produce a PNG image.
If I haven't scared you away by now from using this GDG chapter logo generator, then check it out here: