The acoustic clip was shot by Nathan Poppe in Oklahoma City, and features Kierston White and Camille Harp on backing vocals.
Under Branch & Thorn & Tree is out now via Ramseur Records/Full Time Hobby. It follows 2013's acclaimed record Kid Face.
Crain will play London's The Forge on 11 October - tickets are on sale now.
Watch the "Elk City" performance below.