Are there any good ways to run Steam on a Chromebook?
Solution 1:
As mentioned in the other answer, you could install Linux on your Chromebook. However, this may not be of use because most of the games are processor-specific and will likely require Intel/AMD processors (x64 or x86 instruction set) instead of a Chromebook's ARM processor (completely different instruction set).
Although Steam offers multi-platform gaming, the binaries that are downloaded from Steam are specific to the platforms that Steam offers - Windows, macOS and Linux, and all of those (as far as I know) are Intel-only.
For example, you cannot install Steam on macOS on a PowerPC. Yes Mac OS is supported but ancient Mac OSX is not, and PowerPC is not even though it falls under the "Mac OS" umbrella.
The same is true of your Chromebook. You might be able to get it to run Linux but it won't be the CPU-specific version of Linux (Linux under i686) that Steam supports.
Solution 2:
The only way to nattily install steam on the laptop and run it, by first installing linux
Solution 3:
There are always "ways". But one of the "best" is going to utilize In home Streaming.
First you get steam up and running on a powerful computer, then you install something like crouton, and then steam on the chrome book.
Finally, login to steam on both the powerful machine, and the chrome book, and you can play the game "from" your chromebook, but it's the powerful computer that's doing all the work.
If you don't have a x86 chrome book (most aren't) then you can try stuff like twerk and android streaming apps. They will work but's it's cludgy. See https://www.reddit.com/r/chromeos/comments/3kf73b/psa_you_can_stream_your_gaming_pc_to_your/ for an example.
Finally, though you may not want to hear it, you may be better of with something more dedicated. If you really want to stream to a portable then getting a cheap laptop around $200 and sticking XFCE on it with steam in home streaming is pretty awesome. Your not gonna get CS:GO to be fast enough to be competitive, but Civ 6 will do just fine.
Keep in mind, in all these options, it's the powerful computer that does all the work, not the portable.