I read that ChromeOS was built on the Ubuntu kernel. So how much of the Ubuntu is left? Is X still available? What about a package manager?
No part of ubuntu specifically are included in Chrome (Chromium) OS. Chrome OS uses a modified, linux kernel. It uses a custom display manager (so not X) and a minimal shell called cosh, without any advanced features found in bash.
It uses portage to manage packages (the gentoo package manager).