Generally speaking the Passaic River forms the eastern boundary between Morris and Essex Counties. Chatham is in far eastern Morris County, along the Passaic River and the border of Essex County.
The Passaic River also forms the border between Morris and Somerset County to the south.
Most of the families that Littell covered in his book were located along the eastern Morris western Essex area. Some of the towns he covered (Summit, Millburn, Short HIlls, Springfield, New Providence, Westfield) are now in Union County, which was formed from Essex in 1857. However, since Littell's book was written in 1851, these places were still in Essex County at that time.
It is difficult to describe the area in text, so you might want to check Wikipedia, look at the article on Watchung Mountains.
There was a map prepared by Littell (to accompany his book I guess). I know it covers the Great Swamp area, but don't know about Essex Co. I know there is a copy at the Joint Free Public Library in Morristown (Morris Co.).
Rutgers has many historical NJ maps online athttp://mapmaker.rutgers.edu/MAPS.html
I note that one of Thomas Hallock's sons, Smith Hallock, was living in New Providence, (then in Essex Co.) in 1830 census and also on an 1813 tax list.
I think Essex County is the logical place to look. However, some early records were maintained on the state level. So it might be helpful to know what you are looking for and approximate dates.
If you live in NJ, there are a number of places to research these records. Or if you are near a large genealogy library, there might be people here who could make suggestions.