So I bought a house last year and have realized that the chain-link fence that had been erected (before the purchase) is a mere 14 inches away from our east exterior wall. The fence is just over 4 feet high.
The fence makes it practically impossible to do foundation repair, as well as work on a few vents exiting the basement, and to pull up weeds, which are trapped between the fence and the wall.
The fence for the most part lay directly on the property line, but eases onto my property just slightly as it runs to the back (south side) of the property.
Isn't there some kind of easement of right to work on or maintain the exterior of my building? And if so, can I legally remove this fence, even though my neighbor would want it to remain? What is the process for doing so?

removing fence from property
To the extent the fence is on your property, you can remove it. You should probably have that boundary line surveyed before taking any action. You can follow this link for information about the rights of a property owner to trespass in order to make repairs.