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Only inside a Linux chroot (like Crouton)

You can currently only use web based IDEs or Android based IDEs in Chrome OS.

There are some good web ones (Cloud9) out there and even a few Android based ones (AIDE). You won't be running any Windows or Linux IDEs though (because Chrome OS is not either of those.)

If you're referring to full-blown IntelliJ, Elcipse, VS, etc, the answer is no afaik. But if syntax highlighting, code completion and lightweight refactoring (within and across files) counts, then Caret or Zed might be worth a look. These are native Chrome apps, and don't require web access/connectivity. (I wrote most of the Chromebook piece in the OP and all my Go code using Caret, and am happy with it). I did some toy stress testing by opening up a few copies of War & Peace (1.5M+ line) text files in Caret. It took a couple of seconds to load, but search & replace and rapid scrolling/navigating worked well. Trying the same thing in vim either in Termux natively or via local ssh didn't hiccup at all. As mentioned in other threads, it's a side effect of design decisions, and naive assumptions about in-memory files. Kids today...

Yes it is using Crouton.