I had a similar problem that I had fixed last summer. My chimney was also leaning to the right by at least three inches. It also leaked when it rained and the wind blew from a particular angle. However, it wasnt separating from the house (dont ask me why) it was leaning to the side as it settled over the years. The motor was also disintegrating at the top (the part above the roof line) which is probably why it leaked.
So the contractor I hired (a real chimney contractor not a general contractor) put-up scaffolding and removed the top seventeen courses of brick which just about brought it down to where the chimney attached to the house (or the house attached to the chimney depending how you look at it).
When he had the bricks removed he sawed of the old mortar and cleaned them so they were all nice and square. He then re-laid the bricks keeping everything level and even.
He then installed stainless steel liners all the way from the chimney top to the furnace and fireplace. Poured a new cap at the top and put an epoxy coating on all bricks.
He also replaced a cracked flew liner and replaced that he discovered when he removed the top 17 layers of brick.
Cost: $3,500.00 - Time: about 2 days.