Looking on the [Leo](http://dict.leo.org/#/search=breastfeed&searchLoc=0&resultOrder=basic&multiwordShowSingle=on), the verb *stillen* means to breastfeed.

The English verb contains the word *breast*. Something similar happens in Italian (*allattare*, which contains *latte*-milk). 

What is the etymology of *stillen*? Does it have anything to do with the English word *[still](http://etymonline.com/?term=still)*?