Is it possible to make a vertex group parent to a mesh?
Aha! Found it here!
http://en.wikibooks.org/wiki/Blender_3D:_Noob_to_Pro/Cool_Things#Vertex_Parenting
The instructions are’t very clear. You have to be in edit mode for it to work and also select the other mesh which isn’t in edit mode. The only way I could do this is with the outliner by shift clicking the other mesh in the list.