From looking at .travis.yml, ampproject/amphtml enables sudo: required and uses full VMs with the trusty environment. While these are slow, they guarantee isolation between test instances, and resources allocated for each VM.
It appears that we currently use sudo in one place: to install chrome. If we can do away with the sudo requirement and use Docker containers, we may see a significant speed up in how PR jobs start up on Travis.
The purpose of this issue is to track the feasibility of using Docker containers over full VMs, and if so, to track the work required to make it so.
For reference, see this discussion in #9500