They don't even need to open another tab. There is at least one Google Chrome extension specifically for cheating in chess (which the creators pretty much openly admit - their YT channel features a blatant cheating tutorial video).
I've reported this extension for abuse - since it's obviously unethical, goes against the rules of the websistes it's supposed to be used on, plus the description in the Store is misleading, as it's deliberately vague and unlike their YT profile, it cautiously doesn't mention cheating at all. Obviously it hasn't been taken down though.