Docker mostly works. However, `sudo docker run -it centos bash` fails because the centos image (as do many others) uses extended attributes, which are not compatible with the underlying btrfs filesystem. In those cases, I've been rebuilding the Docker images myself from source, when possible. It's frustratingly close!
wstein@penguin:~$ sudo docker run -it centos bash
Unable to find image 'centos:latest' locally
latest: Pulling from library/centos
a02a4930cb5d: Extracting 75.17MB/75.17MB
docker: failed to register layer: ApplyLayer exit status 1
btrfs definitely supports extended attributes (and if it didn't you'd get ENOTSUP not EPERM when trying to use them). It's far more likely this is because you cannot set certain xattrs within a user namespace (such as some security.* ones) -- and LXC is being used with user namespaces in ChromeOS.
In fact, I added code to Docker almost 4 years ago to ignore ENOTSUP on xattr errors specifically because of filesystem support (AUFS was the issue at the time). So if it was a support issue you wouldn't see it, because the code already handles it. :P
wstein@penguin:~$ sudo docker run -it centos bash
Unable to find image 'centos:latest' locally
latest: Pulling from library/centos
a02a4930cb5d: Extracting 75.17MB/75.17MB
docker: failed to register layer: ApplyLayer exit status 1
stdout: stderr: operation not permitted.
See 'docker run --help'.