Starting next year, Google will provide Chromebook security patches and software upgrades for up to a decade. This will effectively guarantee that no existing Chromebook will expire within the next two years.
However, a Google spokesperson added the caveat that, "In making changes to the expiration policy, we have to coordinate with each partner making any component in these devices. It requires a security and performance guarantee from the makers." Other Google sources indicated that the major Chromebook vendors are expected to work with the company to extend their hardware's lifespan.
Acer Chromebook R 13
Acer Chromebook Spin 311
Asus CX22NA-211.BB01
Been a while since I've looked but I've haven't had much luck finding Linux for those 3.