CPUs definitely has gold (and other metals) in them. I actually read an article about extracting gold from CPUs earlier this year. There is more than $0.10 of gold in your average CPU, it's probably around $0.75 to $1.00 from what I can remember.
The problem is you have to extract the gold on a large scale to actually make it somewhat profitable. And to maximize your profits you should also extract the other metal used CPUs as well such as Aluminum, beryllium, gallium, palladium, platinum, mercury and arsenic (yes, arsenic is considered a metal, or more precisely a metalloid), amongst other metals.
Extracting gold from CPUs, other types of chips and circuit boards can be quite hazardous. You need "Aqua Regia" (Latin for "Royal Water") for this process. "Aqua Regia" is a combination of nitric acid and hydrochloric acid that is mixed in approximately a 1:3 ratio. Those acids are very dangerous to use.
On the plus side, "Aqua Regia" also dissolves platinum as well.
Good luck, don't forget protective gear, and a respirator if you choose to pursue this endeavour.