You will need to be an Administrator on the machine.

1. Open Utilities/Terminal
SHORT VERSION:
2. Type this: sudo chmod go+w /Library/Application\ Support/Propellerhead\ Software/ReWire
CAREFUL, INFORMATIVE VERSION:
2. Type this: cd /Library/Application\ Support/Propellerhead\ Software/
3. Type this: ls -l

You will now see a line something like this:
drwxr-xr-x 7 root wheel 238 Aug 7 22:17 ReWire

4. Type this: sudo chmod go+w ReWire

"chmod go+w" will give the Group and Others the necessary Write access. It will ask for your password, and may give you a warning about using your 'sudo' (Super User) power responsibly. Linux developers are funny guys. Continue...

5. Type this: ls -l

You will now see the line looking more like this:
drwxrwxrwx 7 root wheel 238 Aug 7 22:17 ReWire

Restart and try launching Reason.