Pour yogurt into a strainer lined with a double thickness of cheesecloth and set in a bowl deep enough that the strainer won't sit in liquid. Stir in salt, then lay ends of cheesecloth over yogurt, covering it. Chill at least 1 day and up to 2 (cheese will get denser the longer you drain it).
Spoon cheese into a tall, narrow jar and top with 1/4 in. oil. Labneh keeps, chilled, up to 2 weeks.