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Installing Creative Suite on Mac OS X 10.12 requires a workaround. I would recommend looking over the instructions for installing CS4 on Sierra: Installing Creative Suite on macOS 10.12 (Sierra). Unfortunately, there are no instructions specifically for CS3, since the software too old to have been tested on the newest operating systems.
Let us know if that helps.
I have the same situation with OS X 10.12.5 and CS3... so I am all ears how to continue...
Have you already obtained a new serial number using the instructions here: Download Adobe Creative Suite 3 products? If so, did you follow the instructions for the Sierra workaround posted in my previous reply? If that didn't work for you, it will help us troubleshoot if you can provide some more specifics about what, exactly is happening when you try to install via the workaround.