Is CS3 compatible with macOS Sierra?

Easy upgrade. Just reinstalled the Java Legacy update from Apple as it asks when you try to run the software.

The only reason CS3 requires Java is for the authentication. You can run it from terminal if you don't wish to have java on your system.

How does that work? I'm running java 8, and every time I try to run so or photoshop I get a runtime error telling me to install 6, but when I tried to reinstall java 6 it won't let me cause there is a beer version already uploaded

Photoshop CS3 is working with Sierra as well as it did for me with El Capitan. There may be some features that don't work but none that I use.

However, one must download and apply the Java for OS X 2015-001 installer before PS will work.

Also take a moment to check compatible hardware to see if your precious, fully functional Apple computer is being dropped, even if it could run it. Apple should consider allowing upgrades to older computers without some of the new features that have specific hardware requirements.