Line a baking sheet with paper towels. Rinse the chicken skins, pat them dry, and chop them into 1-inch pieces with a very sharp knife. Arrange them in the largest skillet you have, turn the heat to medium, and cook the skins, stirring more frequently as they begin to brown and lowering the heat if necessary, until the fat renders and the skins are deep golden and crisp, 40 to 45 minutes.

Lift the skins out of the fat with a spider or slotted spoon, letting any extra fat drip into the pan; drain on the paper towel–lined sheet. Season the skins with salt. Store the gribenes in an airtight container for up to 2 weeks, and refrigerate the schmaltz in an airtight container for up to 3 months.

If using a skillet larger than 10 inches in diameter, heat 6 tablespoons of the schmaltz over medium-high heat in the skillet; if not, work in two batches, using half the livers and 3 tablespoons of the schmaltz per batch. Season the livers with 1 teaspoon of the salt and 1/2 teaspoon of the pepper and cook until they are browned on the outside and just barely blushing pink on the inside, 3 minutes per side. 

Remove the livers to a plate, leaving any oil and juices in the pan, then add the onions, raise the heat to high, and cook, stirring, until the onions are charred and softened, 13 to 14 minutes. Transfer to a cutting board and chop (somewhere between roughly and finely) the livers, then the onions, then the eggs.

Transfer everything to a bowl, add the remaining 2 tablespoons schmaltz, stir gently to combine, and season with the remaining 1 teaspoon salt and 1/2 teaspoon pepper. Serve with challah and top with gribenes. Chopped liver can be refrigerated in an airtight container for 4 days.