If the server cannot write to the directory, it probably cannot chmod it either. Its an ownership issue. That is only logical, that does not mean its not possible. He may be right.
You need to make the directory write-able.
Unix/Linux, From the command line:
You can do: chown -R nobody.nobody /path/to/dirnme
or
You can do a 777, but that is not really a good thing to do.
Windows host, your host should provide you with a tool for changing permissions.
WS_FTP also allows you to change file premissions ( server permitting )