Fill a bowl with ice water and salt. Bring a saucepan of water to a boil and lower in eggs with a spoon; cook 6 1/2 minutes for a softly set egg. Transfer eggs to salted ice water (salt helps the shells come off more easily) and cool completely, about 5 minutes. Peel eggs and set aside.
Preheat broiler with a rack set 4 in. from heat. Brush baguette with oil and sprinkle with salt and pepper to taste. Toast bread, turning once, until warm and golden brown, about 5 minutes. Rub cut side of bread with whole lemon to extract oils from peel.
Use a 1 1/2-in. round cutter to cut 4 evenly spaced holes in each baguette half, or use a knife and scoop out with a spoon. Slice bread crosswise between holes into 8 pieces.
Cut eggs in half crosswise and set an egg into each hole. Sprinkle eggs with salt and pepper. Lay 2 anchovies over each and sprinkle with parsley and chives.
*Find in well-stocked grocery stores or Italian markets, or substitute good-quality regular canned or jarred anchovies that you've tossed in a little sherry vinaigrette.