Git will track changes to files and directories, including any changes to permissions done via chmod. In most development environments I tend to have a different set of permissions to those on the live site so I am usually not interested in tracking permissions changes. To prevent git from looking at the difference between the permissions of a file you need to set the core.filemode configuration option to false.
git config core.filemode false
Here is the entry from the git-config(1) manual page.
core.fileMode If false, the executable bit differences between the index and the working tree are ignored; useful on broken filesystems like FAT. See git-update-index(1). The default is true, except git-clone(1) or git-init(1) will probe and set core.fileMode false if appropriate when the repository is created.
This information was originally taken from this post on Stackoverflow. I am always forgetting how to do this, so as an aid to memory I am writing this post.