How does one peel and puree chick peas with a food mill for hummus?
Grinding the chickpeas before cooking kind of defeats the purpose. To use a food mill to its best, you shouldn't do any grinding before you cook the chickpeas.

After you cook them, they will be more accepting of grinding or other techniques. Cook them low and slow just as you would any other bean. When they are tender (and cool enough to handle), put them in the food mill. My food mill only has one coarseness, so I assume that is about medium. So, cook your chickpeas and then use a food mill with the medium blade to remove the skins and proceed with your recipe.