Hi! Just to be sure, you're asking about playing the board game on a computer? Another person on the forum has created a version of the game on a site called Tabletopia:
https://forums.stardewvalley.net/threads/6792/. I haven't tried it out, but it appears to be playable in a browser, which would be possible on a Chromebook.
Another person on the forums created a Tabletop Simulator module for the game:
https://forums.stardewvalley.net/threads/6334/. However, this requires installing Steam and Tabletop Simulator, which I don't think is possible on a Chromebook.