Tree of Heaven," or Ailanthus altissima.
While a mature example is a pretty tree, it has many vices. For instance, Ailanthus tends to make the soil around it toxic to other plant life. Such a tree evolved carefully over the eons to compete with other plants. The Wikipedia entry cited notes the tree's many useful properties, but like mint in the herb garden, a little of this tree goes a long way.
And you can't just have a little of Ailanthus. Here is my "after" picture of the little colony shown above.
National Park Service's page on the tree has many shocking facts. But around here, I've got a couple of groves of the tree where soil was disturbed over the decades.
Control of this plant is not simple. Cutting simply leads to multiplication, like the Hydra of Greek mythology. Spraying is not efficient for huge groves, and I don't use chemicals in that manner.
Yet here my organic practice bends; we have an invasive species out of control. My technique, gleaned from several sources, involves cutting smaller trees to a height where I can treat the stump with Roundup concentrate, using a paint brush and great care to not get chemicals anywhere else.
This needs doing in late summer/early fall or in the spring. A few large trees will get a half-cut to the trunk that runs 2" deep, so I can treat the trunk with Roundup. I plan to check my cuttings for sprouts in Spring and re-treat them. I have to wade into some really "snakey" thickets to get to some of the trees, so snake-proof chaps are mandatory gear.
We'll see if we have fewer next year. Luckily, there are not huge groves here, as one sees along I-64. I'm probably dealing with 100 trees...for now.