Yes it does and I do keep it oiled. I have read that if you pull the wick out there is a tiny pinhole in the base of the wick holder which one can clean out with a fine pin because it can get sealed shut from old oil. I removed the wick and by using a flashlight, took a cottom swab and cleaned it thoroughly and tried to find the pin-size hole. Actually took a small pin and ran around the base and directly down into the bottom but the pin never found an opening. Have you ever tried to do this?