What is having one chronically swollen leg called?

Venous insufficiency. If it is the consequence of a prior venous thrombosis it is called a post-phlebitic leg.
Lymphedema? If you are a woman between the ages of 35 and 55, have a chronically swollen left leg that isn't painful, have no varicose veins, and your foot and toes are swollen too, you probably have a condition called lymphedema. Other things can cause one chronically swollen leg, so seeing a doctor about your leg would be a very good idea.