I have a love-hate relationship with the tree of heaven. I hate that it is so invasive but I have to admire its tenacity to thrive in my tree-deprived, park-poor, coal-fire polluted neighborhood of Chicago. It's a hard life being a tree here where most everything is paved or otherwise impervious, but tree of heaven succeeds.
The five largest trees near our apartment are all tree of heaven.
Ailanthus altissima) is one of the most common trees in Pilsen. It is an extremely vigorous tree able to cope with the difficult conditions of city living such as soil compaction and air pollution. These characteristics make it invasive and capable of displacing native trees. It was introduced from China first to Europe and the to the United States over 200 years ago. It is hard to eradicate from natural areas due to its numerous wind-borne seeds and tendency to resprout from stumps and roots.
The wikipedia article about tree of heaven has a lot of information and can help you identify if you have tree of heaven in your neighborhood. If you live in Chicago, you probably do.