cross threaded header bolt
Problem is sounds like its in the nearly in accessable area of the engine bay. You had not mentioned LT1 or LS1 or any type of engine but if for either cyl head, your going to have to pull the head and if your doing that, just have a machine shop do it since they can make sure its cut right and centered.
I had broken off a header bolt in my LS1 but it was on the driver side and inbetween the # 3 and 5 cyl and was very accessible.



