Bring olive oil, 1 tablespoon vinegar, and water to boil in a large pot. Place artichoke hearts in the mixture, and boil 30 minutes, or until tender; drain.
Prepare Hollandaise Sauce according to recipe directions.
Fill a large saucepan with 3 inches of water. Bring water to a gentle simmer, and add remaining vinegar. Carefully break eggs into simmering water, and allow to cook for 3 to 5 minutes. Yolks should still be soft in center. Remove eggs from water with a slotted spoon and set on a warm plate.
Place artichoke hearts on a serving platter. Place a poached egg on top of each artichoke heart. Cover with hollandaise sauce. Sprinkle olives on top of sauce. Sprinkle chives around platter.
Recipe by Make Mine Gluten Free at https://www.makemineglutenfree.com/eggs-benababs/