In a large pan over medium heat, warm the olive oil. Add the onion and garlic, and sauté for about 10 minutes until the onion is soft and golden.
Increase the heat and add the cleaned chicken livers. Sear them for about 5-7 minutes until they are browned on all sides. Deglaze the pan with white wine and let it evaporate.
Add the chicken broth, anchovies, and capers. Reduce the heat, cover, and simmer for 15-20 minutes until the livers are completely tender. Season the mixture with salt and pepper.