Wash potatoes and leave skin on. In a large food processor, fitted with the shredding disk, shred the potatoes. Over a sink or bowl squeeze the water out of the shredded potatoes, making sure to get as much liquid out as possible.
Transfer to a large bowl, add chives, salt, pepper, eggs and flour. Mix well. In a small nonstick skillet heat 1 tablespoon of butter and oil over moderate heat until foam subsides. Add potato mixture to the skillet. Flatten to make an even layer. Cook the potato cake over moderate heat, turning once and adding another tablespoon of butter. Cook until golden and crisp, about 7 minutes per side. Drain on a paper towel.