Google's Pixelbook Chromebook has been already patched but some other Chromebooks are still vulnerable to the Meltdown bug.
Google has published a table on the Chromium Wiki detailing which devices are vulnerable, which aren't, and which have been patched. You can read it in full here.
If the table says "Yes" or "Not needed" in the column labelled "VE-2017-5754 mitigations (KPTI) on M63" then the device is safe. If it says "no," then it'll need an update to make things right. And if it says "EoL" (end-of-life) then that update is never coming because the device is no longer supported.
Google's own devices are already protected. Meltdown affects mainly Intel processors and Intel-based Chromebooks are safe if they use versions 3.18 or 4.4 of the Linux kernel.