Having some fun, eh, Bill?
The "chips" you need are from Marvell, Broadcom and others. Unfortunately, they only sell them to manufacturers in high volume. So, unless you want 20K units, they are definitely made of Unobtanium.
But Wait!, There's More. Once you obtain the chips, you will need to get the right software. And the software requires licenses and system code that you have to pledge your first born to get.
The may be open source versions of the SW but good luck getting it work on the Unobtainitron.
One approach is to find a small form factor system that is fast enough and runs Linux. Then port a version of Skype to it. Good luck.
Or, you could just use a PC and run Skype on it...