Much as I dislike Chrome....no, it's not?
Chrome is a privacy risk. It's not a security hole in the sense that bad actors can exploit its horribly buggy code and gain privileged access to your system (at least, not commonly that I've heard of).
Chrome is proprietary, to be sure, but it's heavily based on the open-source Chromium.
I'm not aware of Chrome being massively unstable on any common system—however, I freely admit that as I don't use it myself, I might just not be noticing the complaints of others because they don't show up where I would see them.
...Chrome is absolutely a resource hog. No argument there.