They do not. Extensions are required to list out the permissions they need in the manifest file. Go to the options page for managing extensions and enable Developer Mode. Then expand the one you want to check out and get its ID. I believe the following paths are correct though I can only confirm the one for Windows 7. The extension will be a folder with the ID as the name. You can see exactly what it's doing, and even make modifications that will be reflected in the installed extension. Note: any modifications you make will be reverted if there is an update.
Windows XP
C:\Documents and Settings\USERNAME\Local Settings\Application Data\Google\Chrome\User Data\Default\Extensions
Windows Vista
C:\Users\USERNAME\AppData\Local\Google\Chrome\User Data\Default\Extensions
Windows 7
C:\Users\USERNAME\AppData\Local\Google\Chrome\User Data\Default\Extensions
Mac OS X
/Users/username/Library/Application Support/Google/Chrome/Default/Extensions
Comments
They do not. Extensions are required to list out the permissions they need in the manifest file. Go to the options page for managing extensions and enable Developer Mode. Then expand the one you want to check out and get its ID. I believe the following paths are correct though I can only confirm the one for Windows 7. The extension will be a folder with the ID as the name. You can see exactly what it's doing, and even make modifications that will be reflected in the installed extension. Note: any modifications you make will be reverted if there is an update.
Windows XP C:\Documents and Settings\USERNAME\Local Settings\Application Data\Google\Chrome\User Data\Default\Extensions
Windows Vista C:\Users\USERNAME\AppData\Local\Google\Chrome\User Data\Default\Extensions
Windows 7 C:\Users\USERNAME\AppData\Local\Google\Chrome\User Data\Default\Extensions
Mac OS X /Users/username/Library/Application Support/Google/Chrome/Default/Extensions