Drain the artichokes and the piquillo peppers from the liquids they were packed in and set aside. Stack three small butter lettuce leaves and place on each of 4 serving dishes.
Place three or four artichokes in the center of the lettuce stacks, leaving a small space in the center. Place the same amount of the tuna in the center of the artichokes.
Add the salt to the lemon juice and gradually whisk the oil into the lemon juice. Mince the piquillo peppers and add to the dressing. Spoon a few tablespoons of the dressing around each salad and a little on top. Sprinkle with chives and serve.