Peel and slice the onion. Separate the slices into rings.
Pat the livers dry with paper towels, cut them in half, then trim and discard any visible fat or green parts. Wash your hands well after handling the raw livers.
Heat the olive oil over medium heat until it shimmers, about 2 minutes. Add the onions, sprinkle them with ½ teaspoon kosher salt, then fry them, stirring often, until golden-brown, about 10 minutes.
Remove the onions to a plate and cover to keep warm, or place them in the oven on the "keep warm" setting.
In the same skillet, add the cleaned chicken livers. Sprinkle them with ½ teaspoon kosher salt and ¼ teaspoon black pepper.
Cook the livers over medium heat until browned but still pink in the middle, 2-3 minutes per side.
Divide the cooked livers between plates, top with the fried onions, and serve.
1. Nutrition info is based on CalorieKing.com and adjusted for sodium. 2. If added to a too-hot pan, chicken livers will splatter and even burst. So make sure to use medium heat and don't wait too long before adding the livers to the pan.3. The USDA recommends cooking poultry internal organs to an internal temperature of 165 °F.