Turn on the food processor or blender and carefully drop the garlic clove through the chute into the blade(s).
The blade(s) will chop up the garlic quite nicely.
Turn off the machine. Add the basil, chevre.
Begin to pulse, adding the olive oil in a nice stream until you have a creamy paste.
You decide how fluid you want the pesto and add oil accordingly. Taste for seasoning and add salt and pepper as needed.
To store the pesto, place into a small container and pour a layer of olive oil completely over the top. This will eliminate any browning as the surface is sealed off from air. Freeze for future use or refrigerate for up to a week.