Adjust oven rack to upper-middle position and heat oven to 425 degrees. Heat 2 tablespoons chicken fat in 10-inch cast-iron skillet over medium-high heat until shimmering. Add onions and cook, stirring occasionally, until softened, about 3 minutes. Transfer to a bowl and set aside.
Whisk 2 cups water and 2 tablespoons salt in large bowl until salt is dissolved. Fit food processor with the shredding disk. Peel potatoes and halve or quarter lengthwise as needed to fit through the processor feed tube. Shred potatoes. Transfer potatoes to saltwater and toss briefly to coat.
Drain potatoes in a colander. Place one-quarter of shredded potatoes in the center of a clean dish towel. Gather ends of towel and twist tightly to wring out excess moisture from potatoes. Transfer dried potatoes to the now-empty bowl. Repeat 3 more times with remaining potatoes. Stir eggs, pepper, onions, and remaining ¾ teaspoon salt into potatoes until thoroughly combined.
Heat remaining ¼ cup chicken fat in now-empty skillet over medium-high heat until just smoking. Add potato mixture to skillet and distribute it into even layer but do not press down or smooth top. Cook for 1 minute to set bottom.
Transfer to oven and bake until kugel is lightly browned on top, about 45 minutes. Let cool for 5 minutes. Cut into wedges in skillet. Sprinkle with chives and serve.