Remove roots from the leeks and cut in half lengthwise. Rinse under cold water, then slice leeks into 1 inch strips on the diagonal. Heat oil in a pan over medium heat. Add leeks and sauté for 5-7 minutes until they begin to caramelize. Add chopped chard and continue to sauté for another couple minutes. Season with salt & pepper to taste.
Bring a medium pot of water to a boil. Pour 2 Tbsp. of vinegar into the water. Crack open eggs one at a time, into a small bowl. Reduce the heat of that water to gentle simmer.Gently transfer eggs into simmering water. The egg whites will coagulate instantly. Poach the eggs for 3 minutes spooning the simmering water over the eggs. When the whites become opaque and feel firm to the touch they are done. Gently remove eggs with a slotted spoon and lay them on sheets of paper towel to dry. When leeks and chard are done transfer to a serving dish and top with poached eggs.