While working at Guilford Courthouse National Military Park as a member of the Youth Conservation Corps I was taught how to recognize Tree of heaven and spent a few days Seeking and Destroying.
Tree of heaven indeed does have compound leaves. One identifying charactaristic of these leaves is a small lobe on one edge of the leaf, near the base. These are called "nodes".
The other major identifier of tree of heaven is the smell. When cut, the tree gives of a truly sickening stench. I have heard it described as similar to the smell of burning peanuts, but I have never experienced that particular scent, so I can't confirm it. You can remove some leaves of a suspect tree and sniff the broken ends to test the smell. If they assault your nose with their offensive odor, its time to stump and spray.