1. For the poached eggs, fill a large, deep skillet with water. Add vinegar and 1 teaspoon of salt; cover and bring to a gentle boil over medium heat.
2. Break one egg into a small cup. Carefully slip egg into gently boiling water. Repeat with remaining eggs, working in a clockwise direction. Reduce heat; simmer eggs 2 to 3 minutes, until whites are firm near the yolk. Remove with slotted spoon in same order and place in a pan of ice water. Set aside.
3. For the hollandaise sauce, place butter in a 2-cup glass measure. Cover with plastic wrap, turning back one section to vent. Microwave on High 1 to 1-1/2 minutes, until melted. In top of double boiler set above, not in, simmering water, whisk egg yolks and lemon juice until slightly thickened, 1 to 2 minutes. Remove top only of double boiler from water. Whisking constantly, slowly drizzle a few tablespoons melted butter into yolks in a thin, steady stream. Return top of double boiler to simmering water; continue to slowly add butter, whisking constantly, until sauce thickens. Whisk in 1/4 teaspoon salt and red pepper. Cover and remove pan from heat.
4. Heat oven to 300 degrees F. Heat 1 tablespoon butter in large skillet. Add bacon and cook 2 minutes per side, until lightly browned.
5. Divide and spread toasted English muffin halves with remaining 1 tablespoon butter. Place halves on a cookie sheet and keep warm in oven. Return double boiler to stovetop. Whisk 1 tablespoon water into hollandaise sauce. Cover and keep sauce warm over low heat.
6. To reheat poached eggs, bring same skillet filled with fresh water to a boil. Reduce heat to a simmer. Add eggs with slotted spoon and simmer until heated through, about 1 minute.
7. Arrange 2 muffin halves on each of four serving plates. Top each half with a slice of bacon. Remove eggs from simmering water with a slotted spoon, gently shaking off excess water. Place one egg over bacon; divide and spoon hollandaise sauce over each serving. Sprinkle with chives. Makes 4 servings.