The browser plugin requires the machine you're on to have the 1Password app running in the background, which is how it gets its data from the local (and synced) vault. But there is no 1Password ChromeOS app (and I don't think it's really even possible for there to be something like that in ChromeOS), so the browser plugin does not work in Chrome on ChromeOS devices.
A while back, I think the 1Password synced vault files would also have an HTML file you could load up in a browser, which would then communicate locally with the encrypted vault to gain access to your passwords, which was a workaround on ChromeOS. I'm not sure of the security implications of that process, but it isn't supported anymore.
I really like the locally synced vault with browser plugin functionality, but the fact that there isn't a solution on ChromeOS has been a sticking point for me. I've gone the route of having Google store 1Password generated passwords via Chrome's password features, for sites that I regularly access via ChromeOS, which works, but feels excessive.