Place chicken livers in a bowl and cover with filtered water. Using a spoon, or your hands, gently stir the livers under water to rinse them. Drain in a strainer placed in the sink.
Place a large skillet on the stove over medium heat. Add in the duck fat and heat until melted. Once melted, add in the onion, shallot, and garlic. Stirring gently, sweat the alliums until they're just translucent, about 5-8 minutes.
After that, turn the burner to medium-low and add the liver, coconut aminos and salt. Cook gently, stirring periodically and flipping the livers with a spatula so both sides brown evenly, another 5-8 minutes. Once livers are browned**, take the pan off the heat.
Cool the pan for 5 minutes, then transfer the mixture into a blender or food processor. Add in the apple cider vinegar. Blend until the pâté is smooth like mousse. Transfer the pâté into a glass container and let it sit in the fridge overnight, allowing the flavors to develop.
** Livers are done when they have firmed up a bit (you can check by pressing on one or two with your finger or the back of a small spoon), with their outsides clearly browned, and their myoglobin trickling out. If you're unsure, try temping them; the livers are done when their internal temperature reaches 165° F. When cooking meat, I often use a thermometer to double-check my work. I highly recommend this method if you're new to cooking meat, if your immune or digestive system is compromised, or if you're cooking for someone who has a compromised immune or digestive system. Here's the thermometer I use.
Sourcing — Make sure to find a good source for your livers and duck fat. If I’m not buying mine directly from the local farmer’s market, I’m getting them from a co-op like PCC or a natural grocery store like Whole Foods. You can usually find organ meats and cooking fat in the freezer section.