chgrp not permitted

[Dave Howorth <dhoworth@mrc-lmb.cam.ac.uk>]

I'm having trouble changing the group of a directory. I'm sure I'm doing 
something dumb, but I can't spot it :)

dhoworth@pcx36:~$ chgrp www-data tmp
chgrp: changing group of `tmp': Operation not permitted
dhoworth@pcx36:~$ groups dhoworth
dhoworth : dhoworth root adm www-data staff
dhoworth@pcx36:~$ ls -ld tmp
drwxr-xr-x    3 dhoworth dhoworth     4096 Feb 19 11:25 tmp/
dhoworth@pcx36:~$ ls -ld .
drwxr-xr-x   50 dhoworth dhoworth     4096 Feb 24 12:13 ./

I'm the owner of the directory. I belong to the new group. I don't 
understand what's stopping me doing the chgrp?

Thanks, Dave