With a recent push to the SteamVR for Linux page on Github, Valve has announced upcoming SteamVR support for Linux platforms.
It is intended to allow developers to start creating SteamVR content for Linux platforms. Limited hardware support is provided, and pre-release drivers are required. Linux support is currently only available in the "beta" branch, make sure you are using SteamVR[beta] before reporting issues.
The page documents several requirements, including specific graphics drivers (NVIDIA/AMD only, Intel not supported), USB udev rules, and minimum requirements for Unity developers.