Hi Hopper, much depends on how your base molding is installed.
Some bases have a half inch space between it, and the floor.
Even if it doesn't, you'll have to:
First, make a pencil mark to show how high the carpet is against the base. Hopefully the carpet will hide most of the hole in the base.
Pull the carpet back a little right where you want to put your hole.
It should be held down by what's known as 'Tackles strip,' cut away 1 inch the strip, to pass the wire under the carpet.
At the point where the base and floor come together, and below your pencil line, carefully drill into the wall. Check to make sure there are no electrical wire there!
You can also try to run a product like this
http://www.wiremold.com/www/consumer/products/cordmate_2.asp around the top of the base trim, and around the room.