Oooh, this squicks me out just thinking about it, but I think it all depends on where the thing is located?

Basically, the sharpest tool you can find. Disinfect it with rubbing alcohol (or anything you can find really. Something is better than nothing). Stitches would probably be needed, especially if the character doesn't know where the chip is and needs to go digging around for it.

There will be blood.