For the potatoes:
Rinse the potatoes and put them in a large saucepan. Cover them with cold water, add 1 tbsp of salt and bring to a boil. Simmer uncovered for 15 to 20 minutes, until they are just tender. Drain the potatoes in a colander and place a kitchen towel on top, allowing them to steam for 5 to 10 minutes.
For the aioli:
1) Tear the slice of bread into pieces and place in a bowl. Pour the vinegar over the bread, and set aside for 5 minutes.
2) Place the garlic cloves, egg yolks, lemon rind and juice, saffron, 1 1/2 tsp salt and 1/2 tsp pepper in the bowl of a food processor fitted with a steel blade. Add the bread, and puree into a paste. With the processor running, slowly pour the oil into the bowl through the feed tube and process until it is the consistency of thick sour cream. Place in a serving bowl.
3) Slice the potatoes in half and place them on a serving plate. Sprinkle with salt and pepper, and decorate with the chopped chives. Serve with the aioli.