I was using Hamel Husein's 'Claude Save' Chrome extension, but it no longer works because it seems chats are no longer stored in LocalStorage.
If you have ever tried printing (or saving as PDF) a Claude conversation, you'll know that you only get what's currently on the screen.
So I made this, which downloads the conversation as an HTML file which easily be opened, viewed and printed.
I just submitted it to the Chrome Web Store, so it's not available there yet.
Installation instructions are in the README.