You are limited.
How long has this problem been there to the best of your knowledge?
How long have you lived there?
How long has the nighbor lived there?
Are you good friends with the neighbor and want to remain that way?
Yes, it's a "cloud" on both your titles.
First, it would seem that the problem has been there for 21 years and therefore the owner has obtained an easement by presscription in the property to the extent it overhanges into your yard.
The law in Pennsylvania - is generally if a neighbors property encroaches into your yard you can yank the property out by it's roots or whatever to stop/alleviate the encroachment. Things like trees and shrubs are examples of things that will grow back if not yank out by their roots.
You two are going to have to get an attorney to draft an easement for you to file it at the Recorder of Deed Office which will remove the "cloud" on the title for both of you.
The easement only has to be large enough to encompass the encroaching roof and chimney.
I know that you possibly don't like giving up your property - but your stuck and you both should get the problems solved.
DISCLAIMER: Answers from Experts on JustAnswer are not substitutes for the advice of an attorney. JustAnswer is a public forum and questions and responses are not private or confidential or protected by the attorney-client privilege. The Expert above is not your attorney, and the response above is not legal advice. You should not read this response to propose specific action or address specific circumstances, but only to give you a sense of general principles of law that might affect the situation you describe. Application of these general principles to particular circumstances must be done by a lawyer who has spoken with you in confidence, learned all relevant information, and explored various options. Before acting on these general principles, you should hire a lawyer licensed to practice law in the jurisdiction to which your question pertains.
The responses above are from individual Experts, not JustAnswer. The site and services are provided “as is”. To view the verified credential of an Expert, click on the “Verified” symbol in the Expert’s profile. This site is not for emergency questions which should be directed immediately by telephone or in-person to qualified professionals. Please carefully read the Terms of Service (last updated February 8, 2012).