This is an file used for logging and error reporting by Ableton Live. It's used by the Monomodular Installer on both platforms to determine the locations of several Ableton relative folders so that it knows where to put things.
It can be used for error logging when writing Python Remote Control Scripts. It is best viewed by an application that supports real-time updates of file information (Console.app in MacOSX), so that when errors are logged they are immediately viewable.
OSX /Users/"your username"/Library/Preferences/Ableton/Live 8.x.x/Log.txt
If you're using OSX Lion or Mountain Lion, Apple has taken the liberty of hiding the ~/Library folder from us in order to prevent us from hurting ourselves (!). You can still get there in the following way: 1. Click on your Desktop. 2. Press Command+Shift+G 3. Type in "~/Library" (without the quotes) That will take you to your user library folder, from which you can then navigate the rest of the way.
Windows XP/Vista/ C:\Documents and Settings\"your user name"\Application Data\Ableton\Live\Preferences
Windows 7 C:\Users\"your user name"\AppData\Roaming\Ableton\Live 8.x.x\Preferences