Hi David,
Welcome to Microsoft Community.
No, the Microsoft Surface Book 1 keyboard is not compatible with the Surface Book 3. Each generation of the Surface Book has different hardware and design specifications, which means they cannot be interchanged.
If you are looking for a replacement keyboard for your Surface Book 3, you will need to purchase the same version of the Surface Book 3 keyboard as yours, but to avoid potential compatibility issues, I recommend that you get your Microsoft Surface serviced and repaired. How to get service or repair for Surface - Microsoft Support
If you decide to send it in, go to Device service and repair and sign in with your Microsoft account. If your device is already registered, select it and follow the instructions. If your device isn't listed, select Don't see your device? to register it, then follow the instructions to get service.
Through this process, you’ll find out if your Surface is in or out of warranty and how much it’ll cost, if applicable. Depending on the product, the service offered may be a repair or a refurbished replacement. Once an order is created, you’ll get a shipping address so you can send in your device.
I hope this helps. If there is anything not clear, please do not hesitate to let me know.
Your Sincerely
Hahn. W - MSFT | Microsoft Community Support Specialist