GreenArrays and SchmartBoard Make the GA144 Chip Accessible to Experimenters
GreenArrays suggest that the experimenter use the Schmart Board 202-0048-01  for their chip. Schmart Board has a YouTube video  that instructs the experimenter on how to solder a .5 mm pitch QFN chip to their board. GreenArrays also has an application note [pdf]  that goes through the soldering procedure with pictures and text that explains how to do it in more detail. It also explains how to hook up the chip to the external world. There is also a Breadboarding on a Budget  page at GreenArrays that has more help and links to other pages. And don't forget the Documentation and Software  page which can help you plan your project. The page gives you access to development software and a chip simulator which is fully functional and downloadable free of charge.
However, you must be extremely careful to avoid errors when soldering as it is not impossible (in fact it is likely) to overheat the plastic and end up with a useless mess. Do it right the first time. Or the second or third if you are ham handed. I found it amazing that a 13 year old and a 15 year old (mentioned in the pdf) could do it right the first time after getting instructed on the methods to be used. If you do make an error GreenArrays suggests that you finish soldering the chip for practice so you will have a better hand for your next try.
The chip is extremely quiet and can run up to 80 nodes with no decoupling capacitors. This is not recommended AT ALL and was done merely to show how quiet the chip is.
There is much more at the www sites noted above and you should read it all. Have fun! And get those bits banging.