Popularized by the movie, "The Heathers", this phrase is said in response to a request one deems impossible or absurd (much like being gently fucked with a chainsaw). It's basically a way of showing someone how ridiculous what they've just asked sounds.
Ex.
Veronica: “Why can’t we talk to other kinds of people?”
Heather Chandler: “Fuck me gently with a chainsaw. Do I look like Mother Theresa?”
Dylan: "Hey Nick can I borrow your car once its out of the shop?"
"Fuck me gently with a chainsaw. You crashed it just last week!"
New chains means that you changed as a person , same shackles means that you still have (problems , depression ect) and that nearly nothing changed , you still feel as you did before the "new chains".