It depends on how you call chmod.
From man chmod:
chmod never changes the permissions of symbolic links; the chmod system call cannot
change their permissions. This is not a problem since the permissions of symbolic
links are never used. However, for each symbolic link listed on the command line,
chmod changes the permissions of the pointed-to file. In contrast, chmod ignores
symbolic links encountered during recursive directory traversals.
So, if in the first case you run chmod -R 777 directory to recursively change the permissions, the link target will not be affected, but if you do chmod 777 directory/*, it will.
If you change the permissions on the link target directly, those permissions will carry through (since as man page and baraboom say, the actual link permissions aren't used for anything).
Test log for illustration:
$ mkdir dir && touch dir/file{1,2} /tmp/file3 && ln -s {/tmp,dir}/file3
$ ls -l dir/* /tmp/file3
-rw-r--r-- 1 user group 0 2011-06-27 22:02 /tmp/file3
-rw-r--r-- 1 user group 0 2011-06-27 22:02 dir/file1
-rw-r--r-- 1 user group 0 2011-06-27 22:02 dir/file2
lrwxrwxrwx 1 user group 10 2011-06-27 22:02 dir/file3 -> /tmp/file3
$ chmod -R 777 dir && ls -l dir/* /tmp/file3
-rw-r--r-- 1 user group 0 2011-06-27 22:02 /tmp/file3
-rwxrwxrwx 1 user group 0 2011-06-27 22:02 dir/file1
-rwxrwxrwx 1 user group 0 2011-06-27 22:02 dir/file2
lrwxrwxrwx 1 user group 10 2011-06-27 22:02 dir/file3 -> /tmp/file3
$ chmod 700 dir/* && ls -l dir/* /tmp/file3
-rwx------ 1 user group 0 2011-06-27 22:02 /tmp/file3
-rwx------ 1 user group 0 2011-06-27 22:02 dir/file1
-rwx------ 1 user group 0 2011-06-27 22:02 dir/file2
lrwxrwxrwx 1 user group 10 2011-06-27 22:02 dir/file3 -> /tmp/file3