But not, weirdly, at the airport. And they're proud of that. There are all kinds of signs up about how you can buy it at the airport on arrival and carry it in, duty free.

I paid $20 apiece for shots at a bar in Reykjavik. I paid (IIRC) $5 for a bottle at the airport.

(The bars are especially expensive. I'm told that all the Icelanders pre-game before going out drinking. If you plan to drink while in Iceland, pick it up on your way in.)