BG3C LLC seems to be the answer.
Not much on the site yet, besides the logo: http://www.bgc3.com/
But [2] many theories around what this could be:
1. "A way to pay his staff" (according to Wall Street Journal)
2. "a vehicle to coordinate the software mogul's work on his business and philanthropic endeavors", or better yet
3. “Federal trademark filings provide more clues – describing bgC3 as a think tank, under a generic trademark classification that corresponds broadly to areas including “scientific and technological services,” ‘industrial analysis and research,’ and ‘design and development of computer hardware and software.’”
Let's see what BG3C will become in the near future
Links:
[1] http://pulse.veltsos.com/category/it/it-general
[2] http://www.bgc3.com/But