For most modern Linux systems your apache user should not be run as root, and in order to change the ownership of a file or directory, you need to be root. To get around this problem you can use sudo, but be careful with what permissions you give. Here is an example which is working for me:
www-data ALL = NOPASSWD: /bin/chown 1[1-9][0-9][0-9]\:1[1-9][0-9][0-9] /home/www/[a-zA-Z0-9]*
This allows the apache server to change ownership of files in /home/www with name containing a-z, A-Z or numbers (note: no subdirectories). The only valid input of userid is a four digit numeric id, between 1100 and 1999.
Hope this helps.