Japanese honeysuckle (Lonicera japonica), sometimes called "Hall's honeysuckle", is native to Korea and Japan. It was brought to the United States as an ornamental vine sometime in the mid-1800's. Cherished for its large, evergreen leaves, beautiful blossoms and sweet fragrance, it quickly became apparent that the vine would quickly cover and kill any nearby plants. Japanese honeysuckle can grow in almost any environment and is difficult to kill, making it one of the most hated invasive species in America. In fact, as of 1993, it is illegal to sell, distribute or propagate the plant.
Pull on some thick gardening gloves, take up your pruning shears and start clipping the vines. Note that even a small piece of vine, dropped to the ground, can take root. Place discarded vines in a garbage bag, or place them in a pile to burn later.
Cut and untangle the vines from the host plants until you have cut the Japanese honeysuckle back to the stump. Make sure the last cut you make on the stump is a horizontal cut.
Use a large paintbrush to liberally apply a non-selective or broadleaf herbicide to the cut part of the stump. If there are any vines or leaves remaining, cover them as well. You can use the paintbrush again, or spray them until they are dripping wet.
Wait two weeks, then dig up the stump and remove any remaining roots and rhizomes. Even the smallest rhizome can take root again.
Monitor the area during the next growing season, and pull up any seedlings immediately.